You are here:

Turkish Journal of Analysis and Number Theory

ISSN (Print): 2333-1100

ISSN (Online): 2333-1232

Website: http://www.sciepub.com/journal/TJANT

ShareFacebookTwitterLinkedInMendeleyAdd to Delicious

Article

On the Error Term for the Number of Integral Ideals in Galois Extensions

1School of Mathematics, Hefei University of Technology, Hefei, China


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 230-232
DOI: 10.12691/tjant-2-6-8
Copyright © 2014 Science and Education Publishing

Cite this paper:
Sanying Shi. On the Error Term for the Number of Integral Ideals in Galois Extensions. Turkish Journal of Analysis and Number Theory. 2014; 2(6):230-232. doi: 10.12691/tjant-2-6-8.

Correspondence to: Sanying  Shi, School of Mathematics, Hefei University of Technology, Hefei, China. Email: vera123_99@hotmail.com

Abstract

Suppose that E is an algebraic number field over the rational field Let a(n) be the number of integral ideals in E with norm n and Δ(x) denote the remainder term in the asymptotic formula of the l-th integral power sum of a(n). In this paper the bound of the average behavior of Δ(x) is given. This result constitutes an improvement upon that of Lü and Wang for the error terms in mean value.

Keywords

References

[1]  Chandraseknaran K., Good A., On the number of integral ideals in Galois extensions, Monatsh. Math., 95. 99-109. 1983.
 
[2]  Heath-Brown D. R., The number of Abelian groups of order at most x, Journtes Arithmttiques, Luminy 1989.
 
[3]  Huxley M. N., Watt N., The number of ideals in a quadratic field II, Israel J. Math. Part A, 120, 125-153. 2000,
 
[4]  Ivic A., The number of finite non-isomorphic Abelian groups in mean square, Hardy-Ramanujan J., 9, 17-23. 1986.
 
[5]  Ivic A., On the Error Term for the Counting Functions of Finite Abelian Groups, Monatsh. Math. 114, 115-124. 1992.
 
Show More References
[6]  Iwaniec H., Kowalski E., Analytic Number Theory, Amer. Math. Soc. Colloq. Publ., 53, 204-216. 2004.
 
[7]  Landau E., Einführung in die elementare and analytische Theorie der algebraischen Zahlen und der Ideale, Teubner, 1927.
 
[8]  Lü G., Wang Y., Note on the number of integral ideals in Galois extension, Sci. China Ser. A, 53, 2417-2424. 2010.
 
[9]  Müller W., On the distribution of ideals in cubic number fields, Monatsh. Math., 106, 211-219. 1988.
 
[10]  Nowak W.G., On the distribution of integral ideals in algebraic number theory fields, Math. Nachr., 161, 59-74. 1993.
 
Show Less References

Article

Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences

1Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India

2Department of Mathematical Sciences and Computer application, Bundelkhand University, Jhansi (U. P.)

3Department of Mathematics, Mandsaur Institute of Technology, Mandsaur (M. P.) India


Turkish Journal of Analysis and Number Theory. 2014, 2(6), 233-238
DOI: 10.12691/tjant-2-6-9
Copyright © 2014 Science and Education Publishing

Cite this paper:
Yogesh Kumar Gupta, Mamta Singh, Omprakash Sikhwal. Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences. Turkish Journal of Analysis and Number Theory. 2014; 2(6):233-238. doi: 10.12691/tjant-2-6-9.

Correspondence to: Yogesh  Kumar Gupta, Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India. Email: yogeshgupta.880@rediffmail.com

Abstract

The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula Fn=Fn-1+Fn-2, , and F0=0, F1=1, where Fn is a nth number of sequence. Many authors have been defined Fibonacci pattern based sequences which are popularized and known as Fibonacci-Like sequences. In this paper, Generalized Fibonacci-Like sequence is introduced and defined by the recurrence relation Bn=Bn-1+Bn-2, with B0=2s, B1=s+1, where s being a fixed integers. Some identities of Generalized Fibonacci-Like sequence associated with Fibonacci and Lucas sequences are presented by Binet’s formula. Also some determinant identities are discussed.

Keywords

References

[1]  A. F. Horadam: A Generalized Fibonacci Sequence, American Mathematical Monthly, Vol. 68. (5), 1961, 455-459.
 
[2]  A. F. Horadam: Basic Properties of a Certain Generalized Sequence of Numbers, The Fibonacci Quarterly, Vol. 3 (3), 1965, 161-176.
 
[3]  A.T. Benjamin and D. Walton, Counting on Chebyshev polynomials, Math. Mag. 82, 2009, 117-126.
 
[4]  B. Singh, O. Sikhwal and S. Bhatnagar: Fibonacci-Like Sequence and its Properties, Int. J. Contemp. Math. Sciences, Vol. 5 (18), 2010, 859-868.
 
[5]  B. Singh, Omprakash Sikhwal, and Yogesh Kumar Gupta, “Generalized Fibonacci-Lucas Sequence, Turkish Journal of Analysis and Number Theory, Vol.2, No.6. (2014), 193-197.
 
Show More References
[6]  B. Singh, S. Bhatnagar and O. Sikhwal: Fibonacci-Like Sequence, International Journal of Advanced Mathematical Sciences, 1 (3) (2013) 145-151.
 
[7]  D. V. Jaiswal: On a Generalized Fibonacci sequence, Labdev J. Sci. Tech. Part A 7, 1969, 67-71.
 
[8]  M. Edson and O. Yayenie: A New Generalization of Fibonacci sequence and Extended Binet’s Formula, Integers Vol. 9, 2009, 639-654.
 
[9]  M. E. Waddill and L. Sacks: Another Generalized Fibonacci sequence, The Fibonacci Quarterly, Vol. 5 (3), 1967, 209-222.
 
[10]  M. Singh, Y. Gupta, O. Sikhwal, Generalized Fibonacci-Lucas Sequences its Properties, Global Journal of Mathematical Analysis, 2 (3) 2014, 160-168.
 
[11]  M. Singh, Y. Gupta, O. Sikhwal, “Identities of Generalized Fibonacci-Like Sequence.” Turkish Journal of Analysis and Number Theory, vol.2, no. 5 (2014): 170-175. doi:10.12691/tjant 2-5-3.
 
[12]  S. Falcon and A. Plaza: On the Fibonacci K- Numbers, Chaos, Solutions & Fractals, Vol. 32 (5), 2007, 1615-1624.
 
[13]  Singh, M., Sikhwal, O., and Gupta, Y., Generalized Fibonacci-Lucas Polynomials, International Journal of Advanced Mathematical Sciences, 2 (1) (2014), 81-87
 
[14]  S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section, Theory and Applications, Ellis Horwood Ltd., Chichester, 1989.
 
[15]  T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publication, New York (2001).
 
[16]  Y. Gupta, M. Singh, and O. Sikhwal, Generalized Fibonacci-Like Polynomials and Some Identities Global Journal of Mathematical Analysis, 2 (4) (2014) 249-258.
 
Show Less References

Article

An Application of Generalized Bessel Functions on Certain Subclasses of Analytic Functions

1School of Advanced Sciences, VIT University Vellore - 632014, Tamilnadu, India


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 1-6
DOI: 10.12691/tjant-3-1-1
Copyright © 2015 Science and Education Publishing

Cite this paper:
G. Murugusundaramoorthy, T. Janani. An Application of Generalized Bessel Functions on Certain Subclasses of Analytic Functions. Turkish Journal of Analysis and Number Theory. 2015; 3(1):1-6. doi: 10.12691/tjant-3-1-1.

Correspondence to: G.  Murugusundaramoorthy, School of Advanced Sciences, VIT University Vellore - 632014, Tamilnadu, India. Email: gmsmoorthy@yahoo.com

Abstract

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex functions of order α. Further we point out consequences of our main results.

Keywords

References

[1]  O.Altintas and S.Owa, On subclasses of univalent functions with negative coefficients, Pusan Kyŏngnam Math.J., 4 (1988), 41-56.
 
[2]  A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 73 (1-2) (2008), 155-178.
 
[3]  A. Baricz, Geometric properties of generalized Bessel functions of complex order, Mathematica, 48 (71) (1) (2006), 13-18.
 
[4]  A. Baricz,Generalized Bessel functions of the first kind, PhD thesis, Babes-Bolyai University, Cluj-Napoca, (2008).
 
[5]  A. Baricz,Generalized Bessel functions of the first kind, Lecture Notes in Math., Vol. 1994, Springer-Verlag (2010).
 
Show More References
[6]  R.Bharati, R.Parvatham and A.Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J.Math., 6 (1) (1997), 17-32.
 
[7]  T. R. Caplinger and W. M. Causey, A class of univalent functions, Proc. Amer. Math. Soc. 39 (1973), 357-361.
 
[8]  N.E. Cho, S.Y.Woo and S. Owa, Uniform convexity properties for hypergeometric functions, Fract. Cal. Appl. Anal., 5 (3) (2002), 303-313.
 
[9]  K. K. Dixit and S. K. Pal, On a class of univalent functions related to complex order, Indian J. Pure Appl. Math. 26 (9) (1995) 889-896.
 
[10]  A.W.Goodman, On uniformly convex functions, Ann.polon.Math., 56, (1991), 87-92.
 
[11]  A.W.Goodman, On uniformly starlike functions, J.Math.Anal.Appl., 155, (1991), 364-370.
 
[12]  S.Kanas and A. Wi´sniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105 (1999), 327-336.
 
[13]  E. Merkes and B.T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12 (1961), 885-888.
 
[14]  S.R. Mondal and A. Swaminathan, Geometric properties of Generalized Bessel functions, Bull. Malays. Math. Sci. Soc., 35 (1) (2012), 179-194.
 
[15]  A.O.Mostafa, A study on starlike and convex properties for hypergeometric functions, Journal of Inequalities in Pure and Applied Mathematics., 10 (3), Art.87 (2009), 1-8.
 
[16]  G.Murugusundaramoorthy and N.Magesh, On certain subclasses of analytic functions associated with hypergeometric functions, Appl. Math. Letters 24, (2011), 494-500.
 
[17]  K. S. Padmanabhan, On a certain class of functions whose derivatives have a positive real part in the unit disc, Ann. Polon. Math. 23 (1970), 73-81.
 
[18]  S. Ponnusamy and F. Rønning, Duality for Hadamard products applied to certain integral transforms, Complex Variables Theory Appl. 32 (1997), 263-287.
 
[19]  F.Rønning, Uniformly convex functions and a corresponding class of starlike functions, Proc.Amer.Math.Soc., 118, (1993), 189-196.
 
[20]  F.Rønning, Integral representations for bounded starlike functions, Annal.Polon.Math., 60, (1995), 289-297.
 
[21]  H.Silverman, Univalent functions with negative coefficients, Proc.Amer.Math.Soc., 51 (1975), 109-116.
 
[22]  H.Silverman, Starlike and convexity properties for hypergeometric functions, J.Math.Anal.Appl., 172 (1993), 574-581.
 
[23]  K.G.Subramanian, G.Murugusundaramoorthy, P.Balasubrahmanyam and H.Silverman, Subclasses of uniformly convex and uniformly starlike functions. Math. Japonica, 42 (3), (1995), 517-522.
 
[24]  K.G.Subramanian, T.V.Sudharsan, P.Balasubrahmanyam and H.Silverman, Classes of uniformly starlike functions, Publ. Math. Debrecen., 53 (3-4), (1998), 309-315.
 
[25]  A.Swaminathan, Certain suffienct conditions on Gaussian hypergeometric functions, Journal of Inequalities in Pure and Applied Mathematics., 5 (4), Art. 83 (2004), 1-10.
 
Show Less References

Article

Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction

1Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 7-11
DOI: 10.12691/tjant-3-1-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
Bhavana Deshpande, Amrish Handa. Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction. Turkish Journal of Analysis and Number Theory. 2015; 3(1):7-11. doi: 10.12691/tjant-3-1-2.

Correspondence to: Bhavana  Deshpande, Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India. Email: bhavnadeshpande@yahoo.com

Abstract

We introduce the concept of generalized weakly compatibility for the pair {F,G} of mappings F,G:X×X→X and also introduce the concept of common fixed point of the mappings F,G:X×X→X. We establish a common fixed point theorem for generalized weakly compatible pair of mappings F,G:X×X→X without mixed monotone property of any mapping under generalized symmetric Meir-Keeler contraction on a non complete metric space, which is not partially ordered. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

Keywords

References

[1]  V. Berinde, Coupled fixed point theorems for φ-contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 75 (2012), 3218-3228.
 
[2]  V. Berinde and M. Pecurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory Appl. 2012, 2012: 115.
 
[3]  T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006), 1379-1393.
 
[4]  L. Ciric, B. Damjanovic, M. Jleli and B. Samet, Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications, Fixed Point Theory Appl. 2012, 2012:51.
 
[5]  B. Deshpande and A. Handa, Nonlinear mixed monotone-generalized contractions on partially ordered modified intuitionistic fuzzy metric spaces with application to integral equations, Afr. Mat.
 
Show More References
[6]  B. Deshpande and A. Handa, Application of coupled fixed point technique in solving integral equations on modified intuitionistic fuzzy metric spaces, Adv. Fuzzy Syst. Volume 2014, Article ID 348069, 11 pages. 10
 
[7]  H. S. Ding, L. Li and S. Radenovic, Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces, Fixed Point Theory Appl. 2012, 2012:96.
 
[8]  M. E. Gordji, E. Akbartabar, Y. J. Cho and M. Ramezani, Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed Point Theory Appl. 2012, 2012:95.
 
[9]  N. Hussain, M. Abbas, A. Azam and J. Ahmad, Coupled coincidence point results for a generalized compatible pair with applications, Fixed Point Theory Appl. 2014, 2014: 62.
 
[10]  V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (12) (2009), 4341-4349.
 
[11]  A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
 
[12]  M. Mursaleen, S. A. Mohiuddine and R. P. Agarwal, Coupled fixed point theorems for alpha-psi contractive type mappings in partially ordered metric spaces, Fixed Point Theory Appl. 2012, 2012: 228.
 
[13]  B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72, 4508-4517 (2010).
 
[14]  B. Samet, E. Karapinar, H. Aydi and V. C. Rajic, Discussion on some coupled fixed point theorems, Fixed Point Theory Appl. 2013, 2013:50.
 
[15]  W. Sintunavarat, P. Kumam and Y. J. Cho, Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory Appl. 2012, 2012: 170.
 
Show Less References

Article

On the Numerical Regularity in the aspect of Prime Numbers

1Mathematical Society, Foundation Public School, Karachi, Pakistan


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 12-16
DOI: 10.12691/tjant-3-1-3
Copyright © 2015 Science and Education Publishing

Cite this paper:
Shaad P. Sufi. On the Numerical Regularity in the aspect of Prime Numbers. Turkish Journal of Analysis and Number Theory. 2015; 3(1):12-16. doi: 10.12691/tjant-3-1-3.

Correspondence to: Shaad  P. Sufi, Mathematical Society, Foundation Public School, Karachi, Pakistan. Email: shaadpyarali@gmail.com

Abstract

The purpose of this paper is to introduce a new pattern in Primes numbers, to eliminate the randomness in their patterns. This paper also justifies the solutions in a numerical and geometric manner. The Prime Function provides further distinction in the nature of Prime Numbers by distinguishing the nature of normality and Abnormality in Prime Numbers. To verify the normality of corresponding Prime numbers, the Sufi primality test is formed. Also using the Prime Function, the formula for the approximate sum of Prime Numbers is derived. The limitations and conditions of the Prime function are also stated. These factors provide a panoramic view of the Prime Function and its potential factor in Number Theory .

Keywords

References

[1]  https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford /Granville.pdf.
 
[2]  http://annals.math.princeton.edu/2014/179-3/p07.
 
[3]  http://en.wikipedia.org/wiki/Lucas_primality_test.
 

Article

Some Common Fixed Point Theorems for Weakly Contractive Maps in G-Metric Spaces

1Department of Mathematics Guru Jambheshwar University of Science and Technology, Hisar, India


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 17-20
DOI: 10.12691/tjant-3-1-4
Copyright © 2015 Science and Education Publishing

Cite this paper:
Manoj Kumar. Some Common Fixed Point Theorems for Weakly Contractive Maps in G-Metric Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(1):17-20. doi: 10.12691/tjant-3-1-4.

Correspondence to: Manoj  Kumar, Department of Mathematics Guru Jambheshwar University of Science and Technology, Hisar, India. Email: manojantil18@gmail.com

Abstract

In this paper, first we prove a common fixed point theorem for a pair of weakly compatible maps under weak contractive condition. Secondly, we prove common fixed point theorems for weakly compatible mappings along with E.A. and (CLRf) properties.

Keywords

References

[1]  Aamri M. and Moutawakil D. El., Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270, 181-188, 2002.
 
[2]  Aydi H., A fixed point result involving a generalized weakly contractive condition in G-metric spaces, Bulletin of Mathematical Analysis and Applications, vol. 3 Issue 4 (2011), 180-188.
 
[3]  Jungck G., Common fixed points for non-continuous non-self mappings on non-metric spaces, Far East J. Math. Sci. 4 (2), (1996), 199-212.
 
[4]  Khan M.S., Swaleh M. and Sessa S., Fixed point theorems for altering distances between the points, Bull. Aust. Math. Soc. 30 (1) (1984), 1-9.
 
[5]  Mustafa Z. and Sims B., Some remarks concerning D-metric spaces, in Proceedings of the International Conference on Fixed Point Theory and Applications, pp. 189-198, Yokohama, Japan, 2004.
 
Show More References
[6]  Mustafa Z. and Sims B., A new approach to generalized metric spaces, J. Nonlinear and Convex Anal. 7 (2) (2006), 289-297.
 
[7]  Mustafa Z., Obiedat H., and Awawdeh F., Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl. Volume 2008, Article ID 189870, 12 pages, 2008.
 
[8]  Mustafa Z., Shatanawi W. and Bataineh M., Existence of fixed point results in G-metric spaces, International J. Math. Math. Sciences, vol. 2009, Article ID 283028, 10 pages, 2009.
 
[9]  Mustafa Z. and Sims B., Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl. vol. 2009, Article ID 917175, 10 pages, 2009.
 
[10]  Sintunavarat W. and Kumam P., Common Fixed Point Theorems for a Pair of Weakly Compatible mappings in Fuzzy Metric Spaces, Hindawi Publishing Corporation, Journal of Applied mathematics, vol. 2011, Article ID 637958, 14 pages.
 
Show Less References

Article

On the Increasing Monotonicity of a Sequence Originating from Computation of the Probability of Intersecting between a Plane Couple and a Convex Body

1School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China

2College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China

3Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, China


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 21-23
DOI: 10.12691/tjant-3-1-5
Copyright © 2015 Science and Education Publishing

Cite this paper:
BAI-NI GUO, FENG QI. On the Increasing Monotonicity of a Sequence Originating from Computation of the Probability of Intersecting between a Plane Couple and a Convex Body. Turkish Journal of Analysis and Number Theory. 2015; 3(1):21-23. doi: 10.12691/tjant-3-1-5.

Correspondence to: BAI-NI  GUO, School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China. Email: bai.ni.guo@gmail.com, bai.ni.guo@hotmail.com

Abstract

In the paper, the authors confirm the increasing monotonicity of a sequence which originates from the discussion on the probability of intersecting between a plane couple and a convex body.

Keywords

References

[1]  R. D. Atanassov and U. V. Tsoukrovski, Some properties of a class of logarithmically com- pletely monotonic functions, C. R. Acad. Bulgare Sci. 41 (1988), no. 2, 21-23.
 
[2]  C. Berg, Integral representation of some functions related to the gamma function, Mediterr. J. Math. 1 (2004), no. 4, 433-439.
 
[3]  J. Bustoz and M. E. H. Ismail, On gamma function inequalities, Math. Comp. 47 (1986), 659-667.
 
[4]  J. T. Chu, A modified Wallis product and some applications, Amer. Math. Monthly 69 (1962), no. 5, 402-404.
 
[5]  B.-N. Guo and F. Qi, A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 72 (2010), no. 2, 21-30.
 
Show More References
[6]  B.-N. Guo and F. Qi, On the increasing monotonicity of a sequence, ResearchGate Dataset.
 
[7]  J. Gurland, On Wallis’ formula, Amer. Math. Monthly 63 (1956), 643-645.
 
[8]  D. S. Mitrinovi´c, J. E. Peˇcari´c, and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht-Boston-London, 1993.
 
[9]  F. Qi, Bounds for the ratio of two gamma functions, J. Inequal. Appl. 2010 (2010), Article ID 493058, 84 pages.
 
[10]  F. Qi, Bounds for the ratio of two gamma functions: from Gautschi’s and Kershaw’s inequal- ities to complete monotonicity, Turkish J. Anal. Number Theory 2 (2014), no. 5, 152-164.
 
[11]  F. Qi and C.-P. Chen, A complete monotonicity property of the gamma function, J. Math. Anal. Appl. 296 (2004), 603-607.
 
[12]  F. Qi and B.-N. Guo, Wendel’s and Gautschi’s inequalities: Refinements, extensions, and a class of logarithmically completely monotonic functions, Appl. Math. Comput. 205 (2008), no. 1, 281-290.
 
[13]  F. Qi, S. Guo, and B.-N. Guo, Complete monotonicity of some functions involving polygamma functions, J. Comput. Appl. Math. 233 (2010), no. 9, 2149-2160.
 
[14]  F. Qi and Q.-M. Luo, Bounds for the ratio of two gamma functions: from Wendel’s as- ymptotic relation to Elezovi´c-Giordano-Peˇcari´c’s theorem, J. Inequal. Appl. 2013, 2013:542, 20 pages.
 
[15]  F. Qi and Q.-M. Luo, Bounds for the ratio of two gamma functions—From Wendel’s and related inequalities to logarithmically completely monotonic functions, Banach J. Math. Anal. 6 (2012), no. 2, 132-158.
 
[16]  F. Qi, Q.-M. Luo, and B.-N. Guo, Complete monotonicity of a function involving the divided difference of digamma functions, Sci. China Math. 56 (2013), no. 11, 2315-2325.
 
[17]  F. Qi, C.-F. Wei, and B.-N. Guo, Complete monotonicity of a function involving the ratio of gamma functions and applications, Banach J. Math. Anal. 6 (2012), no. 1, 35-44.
 
[18]  R. L. Schilling, R. Song, and Z. Vondraˇcek, Bernstein Functions—Theory and Applications, 2nd ed., de Gruyter Studies in Mathematics 37, Walter de Gruyter, Berlin, Germany, 2012.
 
[19]  D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1946.
 
Show Less References

Article

Fixed Point Results and E. A Property in Dislocated and Dislocated Quasi- metric Spaces

1Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, Albania

2Department of Mathematics, KL University, Green Fields, Andhra Pradesh, India


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 24-29
DOI: 10.12691/tjant-3-1-6
Copyright © 2015 Science and Education Publishing

Cite this paper:
Kastriot Zoto, Arben Isufati, Panda Sumati Kumari. Fixed Point Results and E. A Property in Dislocated and Dislocated Quasi- metric Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(1):24-29. doi: 10.12691/tjant-3-1-6.

Correspondence to: Kastriot  Zoto, Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, Albania. Email: zotokastriot@yahoo.com

Abstract

We prove several fixed points theorems for weakly compatible selfmappings on a dislocated and dislocated quasi-metric space, which satisfy E. A Like and common E. A. Like property, satisfying liner type of contractive condition.

Keywords

References

[1]  Aamri, M. and El Moutawakil, D. Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270, 181-188, 2002.
 
[2]  C. T. Aage and J. N. Salunke. The results on fixed points in dislocated and dislocated quasi-metric space. Appl. Math. Sci.,2(59):2941-2948, 2008.
 
[3]  F. M. Zeyada, G. H. Hassan, and M. A. Ahmed. A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces. The Arabian J. for Sci. and Eng., 31(1A): 111:114, 2005.
 
[4]  G. Jungck and B.E. Rhoades, Fixed points For Set Valued Functions without Continuity, Indian J. Pure Appl. Math., 29 (3) (1998), 227-238.
 
[5]  Liu, W., Wu, J. and Li, Z. Common fixed points of single-valued and multi-valued maps, Int.J. Math. Math. Sc. 19, 3045–3055, 2005.
 
Show More References
[6]  K. Zoto, Weakly compatible mappings and fixed points in dislocated -metric spaces, International journal of mathematical archive, vol. 4 (6), 2013, 131-137.
 
[7]  K. Zoto and E. Hoxha, Fixed point theorems in dislocated and dislocated quasi-metric spaces, Journal of Advanced Studies in Topology; Vol. 3, No.4, 2012.
 
[8]  K. Jha and D. Panthi, A Common Fixed Point Theorem in Dislocated Metric Space, Appl. Math. Sci., vol. 6, 2012, no. 91, 4497-4503.
 
[9]  K. P. R. Rao and P. Rangaswamy, Common Fixed Point Theorem for Four Mappings in Dislocated Quasi-Metric Space, The Nepali Math. Sci. Report, 30 (1-2), 2010, 70-75.
 
[10]  P. Hitzler and A. K. Seda. Dislocated topologies. J. Electr. Engin., 51(12/S):3:7, 2000.
 
[11]  P. S Kumari, Common fixed point theorems on weakly compatible maps on dislocated metric spaces, Mathematical Sciences 2012, 6:71.
 
[12]  R.Shrivastava, Z.K.Ansari and M.Sharma. Some results on Fixed Points in Dislocated and Dislocated Quasi-Metric Spaces. Journal of Advanced Studies in Topology; Vol. 3, No.1, 2012.
 
[13]  S. K. Vats, Weakly Compatible Maps in Metric Spaces, J. Indian Math. Soc., 69 (1-4), (2002), 139-143.
 
[14]  M. Arshad, A. Shoaib and P. Vetro; Common fixed points of a pair of Hardy Rogers type mappings on a closed ball in ordered dislocated metric spaces. Journal of function spaces and applications, vol 2013, article id 638181.
 
[15]  E. Karapinar and P. Salimi, Dislocated metric space to metric-like spaces with fixed point theorems. Fixed Point Theory and Applications 2013, 2013: 222.
 
[16]  M. Arshad, A. Shoaib and I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space. Fixed Point Theory and Applications 2013.
 
[17]  Yijie Ren,Junlei Li, and Yanrong Yu, Common fixed point theorems for nonlinear contractive mappings in dislocated metric spaces. Abstract and Applied Analysis vol 2013, article id 483059.
 
[18]  N. Hussain, J.R. Roshan, V. Parvaneh and M. Abbas; Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications. Journal of Inequalities and Applications 2013, 2013:486.
 
[19]  P Sumati Kumariet al, New Version for Hardy and Rogers Type Mapping in Dislocated Metric Space. International Journal of Basic and Applied Sciences, 1 (4) (2012) 609-617.
 
[20]  K. Jha, D. Panthi; A common Fixed Point Theorem In Dislocated Metric Space, Applied Mathematical Sciences 2012.
 
[21]  K. Wadhwa, H. Dubey, R. Jain; Impact of E. A. Like property on common fixed point theorems in fuzzy metric spaces.J. Adv. Stud. Topology 3 (1) (2012), 52-59.
 
Show Less References

Article

Dirichlet Average of Generalized Miller-Ross Function and Fractional Derivative

1School of Mathematics and Allied Sciences, Jiwaji University, Gwalior

2Department of Mathematics RJIT, BSF Academy, Tekanpur, Gwalior

3Department of Mathematics, National Institute of Technology, Silchar - 788 010, District - Cachar (Assam), India

4L. 1627 Awadh Puri Colony Beniganj, Phase – III, Opposite – Industrial Training Institute (I.T.I.), Faizabad - 224 001 (Uttar Pradesh), India

5Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat – 395 007 (Gujarat), India


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 30-32
DOI: 10.12691/tjant-3-1-7
Copyright © 2015 Science and Education Publishing

Cite this paper:
Mohd. Farman Ali, Manoj Sharma, Lakshmi Narayan Mishra, Vishnu N. Mishra. Dirichlet Average of Generalized Miller-Ross Function and Fractional Derivative. Turkish Journal of Analysis and Number Theory. 2015; 3(1):30-32. doi: 10.12691/tjant-3-1-7.

Correspondence to: Vishnu  N. Mishra, Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat – 395 007 (Gujarat), India. Email: vishnunarayanmishra@gmail.com

Abstract

The object of the present paper is to establish the results of single Dirichlet average of Generalized Miller-Ross Function, using Riemann-Liouville Fractional Integral. The Generalized Miller-Ross Function can be measured as a Dirichlet average and connected with fractional calculus. In this paper the solution comes in compact form of single Dirichlet average of Generalized Miller-Ross Function. The special cases of our results are same as earlier obtained by Saxena et al. [12], for single Dirichlet average of Generalized Miller-Ross Function.

Keywords

References

[1]  Carlson, B.C., Special Function of Applied Mathematics, Academic Press, New York, 1977.
 
[2]  Carlson, B.C., Appell’s function F4 as a double average, SIAM J.Math. Anal. 6 (1975), 960-965.
 
[3]  Carlson, B.C., Hidden symmetries of special functions, SIAM Rev. 12 (1970), 332-345.
 
[4]  Carlson, B.C., Dirichlet averages of x t log x, SIAM J.Math. Anal. 18(2) (1987), 550-565.
 
[5]  Carlson, B.C., A connection between elementary functions and higher transcendental functions, SIAM J. Appl. Math. 17 (1969), 116-140.
 
Show More References
[6]  Deora, Y. and Banerji, P.K., Double Dirichlet average of ex using fractional derivatives, J. Fractional Calculus 3 (1993), 81-86.
 
[7]  Deora, Y. and Banerji, P.K., Double Dirichlet average and fractional derivatives, Rev.Tec.Ing.Univ. Zulia 16 (2) (1993), 157-161.
 
[8]  Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi , F.G., Tables of Integral Transforms, Vol. 2 McGraw-Hill, New York, 1954.
 
[9]  Gupta,S.C. and Agrawal, B.M., Dirichlet average and fractional derivatives, J. Indian Acad.Math. 12(1) (1990), 103-115.
 
[10]  Gupta,S.C. and Agrawal, Double Dirichlet average of ex using fractional derivatives, Ganita Sandesh 5 (1) (1991),47-52.
 
[11]  Mathai, A.M. and Saxena,R.K., The H-Function with Applications in Stastistics and other Disciplines, Wiley Halsted, New York, 1978.
 
[12]  Saxena,R.K., Mathai,A.M and Haubold, H.J., Unified fractional kinetic equation and a fractional diffusion equation, J. Astrophysics and Space Science 209 (2004) , 299-310.
 
[13]  Sharma, Manoj and Jain, Renu, Dirichlet Average and Fractional Derivatie, J. Indian Acad. Math. Vol. 12, No. 1(1990).
 
Show Less References

Article

Moment Problem and Inverse Cauchy Problems for Heat Equation

1Penza State University, Penza, Russia


Turkish Journal of Analysis and Number Theory. 2015, 3(1), 33-36
DOI: 10.12691/tjant-3-1-8
Copyright © 2015 Science and Education Publishing

Cite this paper:
O. Yaremko, N. Yaremko, T. Eliseeva. Moment Problem and Inverse Cauchy Problems for Heat Equation. Turkish Journal of Analysis and Number Theory. 2015; 3(1):33-36. doi: 10.12691/tjant-3-1-8.

Correspondence to: N.  Yaremko, Penza State University, Penza, Russia. Email: yaremki@mail.ru

Abstract

The solution of Hamburger and Stieltjes moment problem can be thought of as the solution of a certain inverse Cauchy problem. The solution of the inverse Cauchy problem for heat equation is founded in the form of Hermite polynomial series. The author reveals, the formulas obtained by him for the solution of inverse Cauchy problem have a symmetry with respect to the formulas for corresponding direct Cauchy problem. Obtained formulas for solution of the inverse problems can serve as a basis for the solution of the moment problem.

Keywords

References

[1]  Akhiezer, N.I., Krein, M.G. Some Questions in the Theory of Moments, Amer. Math. Soc., 1962.
 
[2]  Alifanov, O.M., Inverse problems of heat exchange, M, 1988, p. 279.
 
[3]  Arfken, G. B.; Weber, H. J. (2000), Mathematical Methods for Physicists (5th ed.), Boston, MA: Academic Press.
 
[4]  Bavrin, I. I., Yaremko, O. E. Transformation Operators and Boundary Value Problems in the Theory of Harmonic and Biharmonic Functions (2003) Doklady Mathematics, 68 (3), pp. 371-375.
 
[5]  Baker, G. A., Jr.; and Graves-Morris, P. Padé Approximants. Cambridge U.P., 1996.
 
Show More References
[6]  Beck, J.V., Blackwell, V., Clair, C.R., Inverse Heat Conduction. Ill-Posed Problems, M, 1989, p. 312.
 
[7]  Chebysev, P. Sur les valeurs limites des intégrales, Journal de Mathématiques pures et appliquées, 19 ( 1874), 157-160.
 
[8]  Krein, M.G. and Nudelman, A.A. The Markov Moment Problem and Extermal Problems, Translations of Mathematical Monographs, Volume Fifty, Library of Congress Cataloging in Publication Data, 1977.
 
[9]  Lavrentev, M.M., Some ill-posed problems of mathematical physics, Novosibirsk, AN SSSR, 1962, p. 92.
 
[10]  Mors, F.M., Fishbah, G. Methods of theoretical physics, 1958.
 
[11]  Yaremko, O.E. Matrix integral Fourier transforms for problems with discontinuous coefficients and transformation operators (2007) Doklady Mathematics, 76 (12), pp. 323-325.
 
[12]  Yaremko, O.E. Transformation operator and boundary value problems Differential Equation. Vol.40, No. 8, 2004, pp.1149-1160.
 
Show Less References