Some properties of a class of analytic functions defined by generalized Struve functions

Some properties of a class of analytic functions defined by generalized Struve functions

The aim of this paper is to define a new operator by using the generalized Struve functions ∑∞ n=0 (−c/4)n (3/2)n(k)n z n+1 with k = p+ (b + 2) /2 ̸= 0, −1, −2, . . . and b, c, k ∈ C. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius problems, and some other interesting properties related to this operator.

___

  • Abramowitz M, Stegun IA. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. New York, NY, USA: Dover Publications, 1971.
  • Baricz A, Deniz E, C¸ a˘glar M, Orhan H. Differential subordinations involving generalized Bessel functions. Bull Malays Math Sci Soc 2015; 38: 1255–1280.
  • Dziok J, Srivastava HM. Certain subclasses of analytic functions associated with the generalized hypergeometric function. Integral Transforms Spec Funct 2003; 14: 7–18.
  • Dziok J, Srivastava HM. Classes of analytic functions associated with the generalized hypergeometric function. Appl Math Comput 1999; 103: 1–13.
  • Goodman AW. Univalent Functions, Washington, NJ, USA: Polygonal Publishing House, 1983.
  • Hallenbeck DJ, Ruscheweyh S. Subordination by convex functions. P Am Math Soc 1975; 52: 191–195.
  • Liu MS. On a subclass of p-valent close-to-convex functions of order β and type α. J Math Study 1997; 30: 102–104.
  • Liu MS. On certain subclass of analytic functions. J South China Normal Univ 2002; 4: 15–20.
  • Miller SS, Mocanu PT. Differential Subordinations: Theory and Applications. Series in Pure and Applied Mathematics, No. 225. NewYork, NY, USA: Marcel Dekker, 2000.
  • Orhan H, Ya˘gmur N. Geometric properties of generalized Struve functions. Scientific Annals of “Al I Cuza” University of Iasi (in press).
  • Raina RK, Sharma P. Harmonic univalent functions associated with Wright’s generalized hypergeometric functions. Integral Transforms Spec Funct 2011; 22: 561–572.
  • Shareef Z, Hussain S, Darus M. Convolution operators in the geometric function theory. J Inequal Appl 2012; 2012: 213.
  • Srivastava HM, Attiya AA. An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination. Integral Transforms Spec Funct 2007; 18: 207–216.
  • Ya˘gmur N, Orhan H. Hardy space of generalized Struve functions. Complex Var Elliptic Equ 2014; 59: 929–936.
  • Ya˘gmur N, Orhan H. Starlikeness and convexity of generalized Struve functions. Abstr Appl Anal 2013; 2013: 954513.
  • Zhang S, Jin J. Computation of Special Functions. New York, NY, USA: Wiley Interscience Publication, 1996