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

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

Article

The Rogers-Ramanujan Identities

1Department of Mathematics, University of Chittagong, Bangladesh

2Department of Mathematics, Raozan University College, Bangladesh

3Premier University, Chittagong, Bangladesh


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 37-42
DOI: 10.12691/tjant-3-2-1
Copyright © 2015 Science and Education Publishing

Cite this paper:
Fazlee Hossain, Sabuj Das, Haradhan Kumar Mohajan. The Rogers-Ramanujan Identities. Turkish Journal of Analysis and Number Theory. 2015; 3(2):37-42. doi: 10.12691/tjant-3-2-1.

Correspondence to: Haradhan  Kumar Mohajan, Premier University, Chittagong, Bangladesh. Email: haradhan1971@gmail.com

Abstract

In 1894, Rogers found the two identities for the first time. In 1913, Ramanujan found the two identities later and then the two identities are known as The Rogers-Ramanujan Identities. In 1982, Baxter used the two identities in solving the Hard Hexagon Model in Statistical Mechanics. In 1829 Jacobi proved his triple product identity; it is used in proving The Rogers-Ramanujan Identities. In 1921, Ramanujan used Jacobi’s triple product identity in proving his famous partition congruences. This paper shows how to generate the generating function for C'(n), C1'(n), C''(n), and C1''(n), and shows how to prove the Corollaries 1 and 2 with the help of Jacobi’s triple product identity. This paper shows how to prove the Remark 3 with the help of various auxiliary functions and shows how to prove The Rogers-Ramanujan Identities with help of Ramanujan’s device of the introduction of a second parameter a.

Keywords

References

[1]  Andrews, G.E, “An Introduction to Ramanujan’s Lost Notebook”, American Mathmatical Monthly, 86: 89-108. 1979.
 
[2]  Hardy, G.H. and Wright, E.M. “Introduction to the Theory of Numbers”, 4th Edition, Oxford, Clarendon Press, 1965.
 
[3]  Jacobi, C.G.J. (1829), “Fundamenta Nova Theoriae Functionum Ellipticarum (in Latin), Konigsberg Borntraeger, Cambridge University Press, 2012.
 
[4]  Baxter, R.J., “Exactly Solved Model in Statistical Models”, London, Academic Press, 1982.
 
[5]  Ramanujan, S., “Congruence Properties of Partitions”, Math, Z. 9: 147-153. 1921.
 
Show More References
[6]  Ramanujan, S., “Some Properties of P(n), Number of Partitions of n”, Proc. of the Cam. Philo. Society XIX, 207-210. 1919.
 
[7]  Das, S. and Mohajan, H.K., “Generating Function for P(n,p,*) and P(n, *,p)”, Amer. Rev. of Math. and Sta. 2(1): 33-35. 2014.
 
Show Less References

Article

Some Generalizations of Integral Inequalities of Hermite-Hadamard Type for n-Time Differentiable Functions

1College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China

2School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 43-48
DOI: 10.12691/tjant-3-2-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
Tian-Yu Zhang, Bai-Ni Guo. Some Generalizations of Integral Inequalities of Hermite-Hadamard Type for n-Time Differentiable Functions. Turkish Journal of Analysis and Number Theory. 2015; 3(2):43-48. doi: 10.12691/tjant-3-2-2.

Correspondence to: Bai-Ni  Guo, School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China. Email: bai.ni.guo@hotmail.com

Abstract

In the paper, by establishing two integral identities and Hölder integral inequality, the authors generalize some integral inequalities of Hermite-Hadamard type for n-time differentiable functions on a closed interval.

Keywords

References

[1]  R.-F. Bai, F. Qi, and B.-Y. Xi, Hermite-Hadamard type inequalities for the m- and -logarithmically convex functions, Filomat 27(2013), no. 1, 1-7.
 
[2]  P. Cerone and S. S. Dragomir, Midpoint-type rules from an inequality point of view, Handbook of Analytic-computational Methods in Applied Mathematics, 135-200, Chapman & Hall/CRC, Boca Raton, FL, 2000.
 
[3]  S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Type Inequalities and Applications, RGMIA Monographs, Victoria University, 2000; Available online at http://rgmia.org/monographs/hermite_hadamard.html.
 
[4]  C. P. Niculescu and L.-E. Persson, Convex Functions and their Applications, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 23. Springer, New York, 2006.
 
[5]  F. Qi, Z.-L. Wei, and Q. Yang, Generalizations and refinements of Hermite-Hadamard's inequality, Rocky Mountain J. Math. 35 (2005), no. 1, 235-251.
 
Show More References
[6]  N. Ujević, Some double integral inequalities and applications, Acta Math. Univ. Comenian. (N.S.) 71 (2002), no. 2, 189-199.
 
[7]  B.-Y. Xi and F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applica-tions, Hacet. J. Math. Stat. 42 (2013), no. 3, 243-257.
 
Show Less References

Article

Diagonal Function of k-Lucas Polynomials

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

2Department of Mathematical Science and Computer applications, Bundelkhand University, Jhansi (U. P.) India


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 49-52
DOI: 10.12691/tjant-3-2-3
Copyright © 2015 Science and Education Publishing

Cite this paper:
Yogesh Kumar Gupta, V. H. Badshah, Mamta Singh, Kiran Sisodiya. Diagonal Function of k-Lucas Polynomials. Turkish Journal of Analysis and Number Theory. 2015; 3(2):49-52. doi: 10.12691/tjant-3-2-3.

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

Abstract

The Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, Diagonal function of k-Lucas Polynomials is introduced and defined by Gn+1(x)=kxGn(x)+Gn-2,(x), n≥1. with G0(x)=2. and G1(x)=1 Some Lucas Polynomials, rising & descending diagonal function and generating matrix established and derived by standard methods.

Keywords

References

[1]  A.F Hordam, Diagonal Function, the Fibonacci Quarterly, Vol. 16, 19-36.
 
[2]  Alexandra Lupas Guide of Fibonacci and Lucas polynomials, Octagon Mathematics Magazine Vo. 17, No.1 (1999), 2-12.
 
[3]  B.S.Porov, A note on the sum of Fibonacci and Lucas polynomials, The Fill Quarterly 1970, 428-438.
 
[4]  D.V. Jaiswal, “Some Metric Properties of a Generalized Fibonacci Sequence’’, Labdev Journal of Science and technology, India vol.11-A, No.1, 1973, 1-3.
 
[5]  Jr. V.E. Hoggatt, Fibonacci and Lucas Numbers, Houshton Mifflin Company, Borton, 1965.
 
Show More References
[6]  Koshy, T. Fibonacci and Lucas number with application, Wiley, 2001.
 
[7]  M. Catalan, An Identity for Lucas Polynomials, Fibonacci Quarterly Vol 43, No.1 2005.
 
[8]  Singh, B., S. Teeth, and Harne Diagonal Function of Fibonacci Polynomials, chh. J. Sci. Tech 2005, 97-102.
 
[9]  Vajda, S. Fibonacci and Lucas numbers and the golden section, Ellis Horwood Limited, Chi Chester, England, 1989.
 
[10]  Vorobyou, N.N., The Fibonacci number, D.C. health company, Boston, 1963.
 
Show Less References

Article

Some Common Fixed Point Theorems Satisfying (ψ φ) Maps in Partial Metric Spaces

1Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 53-60
DOI: 10.12691/tjant-3-2-4
Copyright © 2015 Science and Education Publishing

Cite this paper:
Reza Arab. Some Common Fixed Point Theorems Satisfying (ψ φ) Maps in Partial Metric Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(2):53-60. doi: 10.12691/tjant-3-2-4.

Correspondence to: Reza  Arab, Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran. Email: mathreza.arab@iausari.ac.ir

Abstract

In this paper, we present some coincidence and common fixed point results for infinite families of contractive maps satisfying a new class of pairs of generalized contractive type mappings defined in partial metric spaces. Our results extend and generalize many known results in the literature. Also, we introduce an example to support the validity of our results.

Keywords

References

[1]  T. Abdeljawad, E. Karapinar, K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Applied Mathematics Letters, 24(11)(2011),1900-1904.
 
[2]  I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl 2011, 10.
 
[3]  I. Altun, F. Sola, H. Simsek, Generalized contractions on Partial metric spaces, Topology and its Applications. 157 (2010) 2778-2785.
 
[4]  I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J Adv Math Stud. 1, (2008) 1-8.
 
[5]  I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl. 2011.
 
Show More References
[6]  M. Bukatin, R. Kopperman, S. Matthews, H. Pajoohesh, Partial metric spaces, Am. Math. Mon. 116,(2009) 708-718.
 
[7]  E. Karapinar, M. E. Inci, Fixed point theorems for operators on partial metric spaces, Appl Math Lett 24 (11)(2011) 1894-1899.
 
[8]  S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197.
 
[9]  S. Oltra, O. Valero, Banachs fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste 36 (2004) 17-26.
 
[10]  S. J. ONeill, Two topologies are better than one, Tech. report, University of Warwick, Coven-try, UK, http://www.dcs.warwick.ac.uk/reports/283.html, 1995.
 
[11]  S. J. ONeill, Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 806, 1996, pp. 304-315.
 
[12]  S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. 2010 (Ar-ticle ID 493298),6 (2010).
 
[13]  S. Romaguera, O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Math. Structures Comput. Sci. 19 (3) (2009), 541-563.
 
[14]  B. Samet, M. Rajovic, R. Lazovi, R. Stoiljkovic, Common Fixed Point Results For Nonlinear Contractions in Ordered Partial Metric Spaces, Fixed Point Theory Appl. 2011.
 
[15]  O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol, 6 (2) (2005) 229-240.
 
Show Less References

Article

On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application

1Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Malaysia

2Department of Mathematics, University of Hail, 2440, Saudi Arabia


Turkish Journal of Analysis and Number Theory. 2015, 3(2), 61-67
DOI: 10.12691/tjant-3-2-5
Copyright © 2015 Science and Education Publishing

Cite this paper:
A. Qayyum, M. Shoaib, I. Faye. On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application. Turkish Journal of Analysis and Number Theory. 2015; 3(2):61-67. doi: 10.12691/tjant-3-2-5.

Correspondence to: I.  Faye, Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Malaysia. Email: ibrahima_faye@petronas.com.my

Abstract

The aim of this paper is to establish new inequalities using weight function which generalizes the inequalities of Dragomir, Wang and Cerone. In this article we obtain bounds for the deviation of a function from a combination of weighted integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as particular instances of the current development. Applications for cumulative distribution function is also discussed.

Keywords

References

[1]  P. Cerone, A new Ostrowski type inequality involving integral Means over end intervals, Tamkang Journal Of Mathematics Volume 33, Number 2, 2002.
 
[2]  P. Cerone and S.S. Dragomir, Trapezoidal type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, CRC Press N.Y. (2000).
 
[3]  X. L. Cheng, Improvement of some Ostrowski-Grüss type inequalities, Comput. Math. Appl. 42 (2001), 109 114.
 
[4]  S. S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, V.U.T., 1(1999), 67-76.
 
[5]  S. S. Dragomir and S. Wang, A new inequality Ostrowski’s type in Lp-norm, Indian J. of Math. 40 (1998), 299-304.
 
Show More References
[6]  S. S. Dragomir and S. Wang, A new inequality Ostrowski’s type in L1-norm and applications to some special means and some numerical quadrature rules, Tamkang J. of Math. 28(1997), 239-244.
 
[7]  S. S. Dragomir and S. Wang, An inequality Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Math. Applic. 33(1997), 15-22.
 
[8]  S. S. Dragomir and S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and to some numerical quadrature rules, Appl. Math.Lett. 11(1998), 105-109.
 
[9]  S. S. Dragomir and S. Wang, An inequality of Ostrowski-Grüs type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (11), 15-20, (1997).
 
[10]  Z. Liu, Some companions of an Ostrowski type inequality and application, J. Inequal. in Pure and Appl. Math, 10(2), 2009, Art. 52.
 
[11]  G. V. Milovanovicˊ and J. E. Pecaricˊ, On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (544-576), 155-158, (1976).
 
[12]  D. S. Mitrinovicˊ, J. E. Pecaricˊ and A. M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, 1994.
 
[13]  A.Ostrowski, Uber die Absolutabweichung einer di erentienbaren Funktionen von ihren Integralimittelwert, Comment. Math. Hel. 10 (1938), 226-227.
 
[14]  A. Qayyum, M. Shoaib, A. E. Matouk, and M. A. Latif, On New Generalized Ostrowski Type Integral inequalities, Abstract and Applied Analysis, Volume 2014, Article ID 275806.
 
[15]  A. Qayyum, M. Shoaib, and I. Faye, Some New Generalized Results on Ostrowski Type Integral Inequalities With Application, Journal of computational analysis and applications, vol. 19, No.4, 2015.
 
[16]  A. Qayyum, I. Faye, M. Shoaib, M.A. Latif, A Generalization of ostrowski type inequality for mappings whose second derivatives belong to L1(a,b) and applications, International Journal of Pure and Applied Mathematics, 98 (2) 2015, 169-180.
 
[17]  A. Qayyum, M. Shoaib, M.A. Latif, A Generalized inequality of Ostrowski type for twice differentiable bounded mappings and applications, Applied Mathematical Sciences, Vol. 8, 2014, (38), 1889-1901.
 
Show Less References