Coefficient bounds and distortion theorems for the certain analytic functions

Abstract

In this paper, we introduce and investigate an analytic function class Pq(λ, A, B) that we call the class of q− starlike and q− convex functions with respect to the parameter λ. We give coefficient bounds estimates, distortion bound and growth theorems for the functions belonging to this class.

Bohr Radius Problems for Some Classes of Analytic Functions Using Quantum Calculus Approach

“…Note that there is a typing error in the statement of [31] (Theorem 3.1, p. 993) (replace α by β). The correct statement in Lemma 6 is as follows:…”

On Generalizations of the Close-to-Convex Functions Associated with q-Srivastava–Attiya Operator

“…This was the amazing breakthrough by which two different fields, q-calculus and the theory of analytic functions, were linked. After this interesting investigation, certain subclasses of analytic functions were defined and examined in terms of q-function theory by several scholars; we refer to [21][22][23][24][25][26][27][28][29][30]. The study of q-operators plays a vital role in the development of this field of study.…”

Coefficient estimates for the class of quasi q-convex functions

“…Quasi-starlike and quasi-convex functions were studied by Altıntaş (see [1]). Altıntaş and Mustafa studied q -starlike and q -convex functions (see [2]). We have the following properties: Remark 1.…”

“…(see [2].Corallary 2.5) Definition 1.6 A function f (z) ∈ A in the form of (1.1) is said to be in the class P q (λ, β, A, B) if the following condition is satisfied:…”