##### You are here:

Turkish Journal of Analysis and Number Theory

## 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. | ||

## Article

# The Rogers-Ramanujan Identities

^{1}Department of Mathematics, University of Chittagong, Bangladesh

^{2}Department of Mathematics, Raozan University College, Bangladesh

^{3}Premier 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

_{1}'(n), C''(n), and C

_{1}''(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”, 4^{th} 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. | ||

[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. | ||

## Article

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

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

^{2}School 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

## 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. | ||

[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. | ||

## Someone is Doing on SciEP

## Statistics of This Journal

Article Downloads: 103510

Article Views: 360595

## Sponsors, Associates, and Links

To list your link on our website, please
click here
or
contact us

New horizons in basic and applied science