Abstract
In this paper, making use of the q-R uscheweyh differential operator , and the notion of t h e J anowski f unction, we study some subclasses of holomorphic f- unction s . Moreover , we obtain so me geometric characterization like co efficient es timat es , rad ii of starlikeness ,distortion theorem , close- t o- convexity , con vexity, ext reme point s, neighborhoods, and the i nte gral mean inequalities of func tions affiliation to these c lasses
Highlights
Let represents the class of functions {| | } and of the form which are holomorphic functions in the unit disc ∑The subclass of A consisting of univalent functions is denoted by S
We provide some fundamental definitions and results of q -calculus which we shall apply in our results
We note the following: (i) For the class reduces to the class discussed by Agrawal and Sahoo [17]
Summary
The subclass of A consisting of univalent functions is denoted by S. A function in is said to be starlike of order in if this condition satisfies. A given holomorphic function with is said to be in the class [ ] , if and only if the following condition satisfies: Geometrically, the function [ ] maps the unit disk onto the domain [ ]defined by l2. For the applications of q-calculus in geometric function theory, one may refer to the papers of Mohamad and Darus [8], Mohamad and. The application of q-calculus was initiated by Jacks n [13] ( see [14,15]) in ge metric function theory. The q-generalized Pochhamer symbol for is defined as [ ] {[ ][ Let be the function given as. The differential q-Ruscheweyh operator and for given by ( 1) is defined as of order
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