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Turkish Journal of Analysis and Number Theory

## Article

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

^{1,}

^{1}School 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

## 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. | ||

[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. | ||

## Article

# Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences

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

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

^{3}Department 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

_{n}

_{=}F

_{n}

_{-1}+F

_{n}

_{-2, }, and F

_{0}=0, F

_{1}=1, where F

_{n}is a n

^{th }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 B

_{n}

_{=}B

_{n}

_{-1}+B

_{n}

_{-2,}with B

_{0}=2s, B

_{1}=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. | ||

[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. | ||

## Article

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

^{1}School 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

## 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). | ||

[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. | ||

## Article

# Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction

^{1}Department 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

## 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. | ||

[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. | ||

## Article

# On the Numerical Regularity in the aspect of Prime Numbers

^{1,}

^{1}Mathematical 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

## 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

^{1,}

^{1}Department 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

## 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. | ||

[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. | ||

## Article

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

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

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

^{3}Department 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

## 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. | ||

[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. | ||

## Article

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

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

^{2}Department 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

## 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. | ||

[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. | ||

## Article

# Dirichlet Average of Generalized Miller-Ross Function and Fractional Derivative

^{1}School of Mathematics and Allied Sciences, Jiwaji University, Gwalior

^{2}Department of Mathematics RJIT, BSF Academy, Tekanpur, Gwalior

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

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

^{5}Applied 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

## Keywords

## References

[1] | Carlson, B.C., Special Function of Applied Mathematics, Academic Press, New York, 1977. | ||

[2] | Carlson, B.C., Appell’s function F_{4} 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. | ||

[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). | ||

## Article

# Moment Problem and Inverse Cauchy Problems for Heat Equation

^{1}Penza 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

## 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. | ||

[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. | ||

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