Abstract
In this paper, we consider a new class of analytic functions which is defined by means of a Ruscheweyh q-differential operator. We investigated some new results such as coefficients inequalities and other interesting properties of this class. Comparison of new results with those that were obtained in earlier investigation are given as Corollaries.
Highlights
Let A denote the class of functions f analytic in the open unit diskE = {z : z ∈ C and |z| < 1} and satisfying the normalization condition f (0) = 0 and f (0) = 1.Received 2017-09-25; accepted 2017-12-07; published 2018-03-07. 2010 Mathematics Subject Classification
We consider a new class of analytic functions which is defined by means of a Ruscheweyh q-differential operator
We investigated some new results such as coefficients inequalities and other interesting properties of this class
Summary
Analytic functions; Ruscheweyh q-differential operator; q-derivative operator; conic domains. The extremal functions for these conic regions are. The function p ∈ k − P [A, B] takes all values from the domain Ωk[A, B], −1 ≤ B < A ≤ 1, k ≥ 0 which is defined as: Ωk[A, B] = w :. B2 − 1 u2 + v2 − 2 (AB − 1) u + A2 − 1 2 > k −2 (B + 1) u2 + v2 + 2 (A + B + 2) u − 2 (A + 1) 2 + 4 (A − B) v2 This domain represents the conic type regains for detail see [11]. Throughout this paper we assume q to be a fixed number between 0 and 1. For any non-negative integer n, the q-integer number n, [n, q] is defined by:. The q-number shifted factorial is defined by [0, q]!
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