A certain subclass of uniformly convex functions defined by Bessel functions
DOI:
https://doi.org/10.22199/issn.0717-6279-2019-04-0047Keywords:
Analytic function, Bessel function, Starlike, Subordination and Hadamard productAbstract
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.Downloads
References
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/2OvSxcO
A. Baricz, Generalized Bessel functions of the first kind, Ph. D. thesis, Babes-Bolyai University, Cluj-Napoca, Rumania, 2008.
A. Baricz, Generalized Bessel functions of the first kind, vol. 1994. Heidelberg: Springer, 2010, doi: 10.1007/978-3-642-12230-9
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
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.
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/312bfeX
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
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.
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.
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.
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.
G. Murugusundaramoorthy, K. Vijaya and M. Kasturi, A note on subclasses of starlike and convex functions associated with Bessel functions, J. Nonlinear Funct. Anal., vol. 2014, 11, Apr. 2014. [On line]. Available: https://bit.ly/2LYanDE
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.
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/311j6tg
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
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.
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.
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.
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/327OqI0
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.
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/3118AlB
Downloads
Published
Issue
Section
License
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
