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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0047 

Articles

A certain subclass of uniformly convex functions defined by Bessel functions

1Kakatiya University, Dept. of Mathematics, Warangal, TG, India. e-mail: reddypt2@gmail.com

2GITAM University, Dept. of Mathematics, GST, Doddaballapur, KA, India. e-mail: bvlmaths@gmail.com

Abstract

The aim of the present paper is to investigate some characterization for generalized Bessel functions of the first kind is to be a subclass of analytic functions. Furthermore, we studied coefficient estimates, radius of starlikeness, convexity, close - to - convexity, convex linear combinations for the class T S(λ, γ). Finally we proved Integral means inequalities for the class.

Keywords: Analytic function; Bessel function; Starlike; Subordination and Hadamard product.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgements

The authors would like to express sincere thanks to the esteemed Referee(s) for their careful readings, valuable suggestions and comments, which helped them to improve the presentation of this paper.

References

[1] A. Baricz, “Geometric properties of generalized Bessel function”, Publicationes Mathematicae, vol. 73, no. 1-2, pp. 155-178, 2008. [On line]. Available: https://bit.ly/2OvSxcOLinks ]

[2] A. Baricz, Generalized Bessel functions of the first kind, Ph. D. thesis, Babes-Bolyai University, Cluj-Napoca, Rumania, 2008. [ Links ]

[3] A. Baricz ,Generalized Bessel functions of the first kind , vol. 1994. Heidelberg: Springer, 2010, doi: 10.1007/978-3-642-12230-9 [ Links ]

[4] A. Baricz and B. Frasin, “Univalence of integral operators involving Bessel functions”, Applied mathematics letters, vol. 23, no. 4, pp. 371-376, Apr. 2010, doi: 10.1016/j.aml.2009.10.013 [ Links ]

[5] A. Baricz , E. Deniz, M. Caglar and H. Orhan, “Differential subordinations involving generalized Bessels functions”, Bulletin of the malaysian mathematical sciences society, vol. 38, no. 3, pp. 1255-1280, Jul. 2015, doi: 10.1007/s40840-014-0079-8. [ Links ]

[6] N. Cho, H. Lee and R. Srivastava, “Characterizations for certain subclasses of starlike and convex functions associated with Bessel functions”, Filomat, vol. 30, no. 7, pp. 1911-1917, 2016. [On line]. Available: https://bit.ly/312bfeXLinks ]

[7] E. Deniz , H. Orhan and H. Srivastava, “Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions”, Taiwanese journal of mathematics, vol. 15, no. 2, pp. 883-917, Apr. 2011, doi: 10.11650/twjm/1500406240 [ Links ]

[8] E. Deniz , “Convexity of integral operators involving generalized Bessel functions”, Integral transforms and special functions, vol. 24, no. 3, pp. 201-216, May 2013, doi: 10.1080/10652469.2012.685938. [ Links ]

[9] S. Kanas and A. Wisniowska, “Conic regions and K-uniform convexity”, Journal of computational and applied mathematics, vol. 105, no. 1-2, pp. 327-336, May 1999, doi: 10.1016/S0377-0427(99)00018-7. [ Links ]

[10] J. Littlewood, “On inequalities in the theory of functions”, Proceeding of the London mathematical society, Vol. s2-23, no. 1, pp. 481-519, 1925, doi: 10.1112/plms/s2-23.1.481. [ Links ]

[11] G. Murugusundaramoorthy and N. Magesh, “On certain subclasses of analytic functions associated with hypergeometric functions”, Applied mathematics letters , vol. 24, no. 4, pp. 494-500, Apr. 2011, doi: 10.1016/j.aml.2010.10.048. [ Links ]

[12] G. Murugusundaramoorthy , K. Vijaya and M. Kasturi, A note on subclasses of starlike and convex functions associated with Bessel functions, Journal of nonlinear functional analysis, vol. 2014, no, 11, Apr. 2014. [On line]. Available: https://bit.ly/2LYanDELinks ]

[13] G. Murugusundaramoorthy and T. Janani, “An application of generalized Bessel functions on certain subclasses of analytic functions”, Turkish journal of analysis and number theory, vol. 3, no. 1, pp. 1-6, 2015, doi: 10.12691/tjant-3-1-1. [ Links ]

[14] S. Porwal and K. Dixit, “An application of generalized Bessel functions on certain analytic functions”, Acta Universitatis matthiae belii series mathematics, vol. 21, pp. 51-57, 2013. [On line]. Available: https://bit.ly/311j6tgLinks ]

[15] C. Ramachandran, K. Dhanalakshmi and V. Lakshminarayanan, “Certain aspects of univalent function with negative coefficients defined by Bessel function”, Brazilian archives of biology and technology, vol. 59, no. special 2, pp. 1-14, 2016, doi: 10.1590/1678-4324-2016161044 [ Links ]

[16] T. Shanmugam, “Hypergeometric functions in the geometric function theory”, Applied mathematics computation, vol. 187, no. 1, pp. 433-444, Apr. 2007, doi: 10.1016/j.amc.2006.08.143. [ Links ]

[17] H. Silverman, “Univalent functions with negative coefficients”, Proceedings of the American mathematical society, vol. 51, pp. 109-116, 1975, doi: 10.1090/S0002-9939-1975-0369678-0. [ Links ]

[18] H. Silverman, “A survey with open problems on univalent functions whose coefficient are negative”, Rocky Mountain journal of mathematics, vol. 21, no. 3, pp. 1099-1125, 1991, doi: 10.1216/rmjm/1181072932. [ Links ]

[19] H. Silverman, “Integral means for univalent functions with negative coefficient”, Houston journal of mathematics , vol. 23, no. 1, pp. 169-174, 1997. [On line]. Available: https://bit.ly/327OqI0Links ]

[20] S. Sivasubramanian, T. Rosy and K. Muthunagai, “Certain sufficient conditions for a subclass of analytic functions involving Hohlov operator”, Computers & mathematics with applications, vol. 62, no. 12, pp. 4479-4485, Dec. 2011, doi: 10.1016/j.camwa.2011.10.025. [ Links ]

[21] P. Thirupathi and B. Venkateshwarlou, “On a certain subclass of uniformly convex functions defined by Bessel functions”, Transylvanian journal of mathematics and mechanics, vol. 10, no. 1, pp. 43-49, 2018. [On line]. Available: https://bit.ly/3118AlBLinks ]

Received: August 2018; Accepted: October 2018

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