Subclasses of uniformly convex and starlike functions associated with Bessel functions

Subclasses of uniformly convex and starlike functions associated with Bessel functions

In recent years, applications of Bessel differential equations have been commonly used in univalent functionstheory. The main object of the present paper is to give some characteristic properties for some subclasses of uniformlystarlike and convex functions which are defined here by means of the normalized form of the generalized Bessel function tobe univalent in the open unit disc. Furthermore, we also establish some results of these subclasses related to a particularintegral operator. Some corresponding consequences of our main results are also considered.

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  • [1] Akgül A. On second-order differential subordinations for a class of analytic functions defined by convolution. Journal of Nonlinear Sciences and Applications 2017; 10: 954-963.
  • [2] Akgül A. Second-order differential subordinations on a class of analytic functions defined by the Rafid Operator. Ukrainian Mathematical Journal 2018; 70(5): 673-686.
  • [3] Baricz Á. Geometric properties of generalized Bessel functions of complex order. Mathematica 2006; 48 (71): 13-18.
  • [4] Baricz Á. Geometric properties of generalized Bessel functions. Publicationes Mathematicae 2008; 73: 155-178.
  • [5] Baricz Á. Generalized Bessel functions of the first kind. PhD, Babes-Bolyai University, Cluj-Napoca, Romania, 2008.
  • [6] Baricz Á. Generalized Bessel Functions of the First Kind. New York, NY, USA: Springer, 2010.
  • [7] Bharati R, Parvatham R, Swaminathan A. On subclasses of uniformly convex functions and corresponding class of starlike functions. Tamkang Journal of Mathematics 1997; 28: 17-32.
  • [8] Cho NE, Lee HJ, Srivastava R. Characterizations for certain subclasses of starlike and convex functions associated with Bessel functions. Filomat 2016; 30 (7): 1911-1917.
  • [9] Choi J, Agarwal P. Certain unified integrals involving a product of Bessel functions of the first kind. Honam Mathematical Journal 2013; 35 (4): 667-677.
  • [10] Deniz E, Orhan H, Srivastava HM. Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions. Taiwanese Journal of Mathematics 2011; 15 (2): 883-917.
  • [11] Deniz E. Convexity of integral operators involving generalized Bessel functions. Integral Transforms and Special Functions 2013; 24 (3): 201-216.
  • [12] Goodman AW. On uniformly convex functions. Annales Polonici Mathematici 1991; 56 (1): 87-92.
  • [13] Goodman AW. On uniformly starlike functions. Journal of Mathematical Analysis and Applications 1991; 155 (2): 364-370.
  • [14] Ma W, Minda D. Uniformly convex functions. In Annales Polonici Mathematici 1992; 57 (2): 165-175.
  • [15] Mondal SR, Swaminathan A. Geometric Properties of Generalized Bessel Functions. Bulletin of the Malaysian Mathematical Sciences Society 2012; 35 (1).
  • [16] Rønning F. On starlike functions associated with parabolic regions. Annales Universitatis Mariae Curie-Sklodowska Section A 1991; 45 (14): 117-122.
  • [17] Rønning F. Uniformly convex functions and a corresponding class of starlike functions. Proceedings of the American Mathematical Society 1993; 118 (1): 189-196.
  • [18] Sakar FM, Aydogan SM. Subclass of m-quasiconformal Harmonic Functions in Association with Janowski Starlike Functions. Applied Mathematics and Computation 2018; 319: 461-468.
  • [19] Silverman H. Univalent functions with negative coefficients. Proceedings of the American Mathematical Society 1975; 51 (1): 109-116.
  • [20] Srivastava HM, Murugusundaramoorthy G, Janani T. Uniformly star-like functions and uniformly convex functions associated with the Struve function. Journal of Applied and Computational Mathematics 2014; 3-16.