Certain subclasses of analytic functions defined by a new general linear operator. (English) Zbl 1409.30015
Summary: Hypergeometric functions are of special interests among the complex analysts especially in looking at the properties and criteria of univalent. Hypergeometric functions have been around since 1900’s and have special applications according to their own needs. Recently, we had an opportunity to study on \(q\)-hypergeometric functions and quite interesting to see the behavior of the functions in the complex plane. There are many different versions by addition of parameters and choosing suitable variables in order to impose new set of \(q\)-hypergeometric functions. The aim of this paper is to study and introduce a new convolution operator of \(q\)-hypergeometric typed. Further, we consider certain subclasses of starlike functions of complex order. We derive some geometric properties like, coefficient bounds, distortion results, extreme points and the Fekete-Szego inequality for these subclasses.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
Keywords:
analytic functions; univalent functions; star-like functions; linear operator; Fekete-Szego problemReferences:
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