Generalized q-starlike functions

Abstract

In this paper, we introduce a new concept of q-bounded radius rotation and define the class R*m(q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S*q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.

On Analytic Functions Involving the q-Ruscheweyeh Derivative

“…Then, I n f ∈ S * q (n + 1, α). For q → 1 − , (20) represents Bernardi operator, see Reference [24].…”

“…Here, we give some basic definitions and results of q-calculus which we shall use in our results. For more details, see References [12,13,[17][18][19][20][21][22].…”

Study on the q-analogue of a certain family of linear operators

“…Some properties related with q-function theory were first introduced by Ismail et al [11]. Moreover, several authors studied many applications of q-calculus associated with generalized subclasses of analytic functions; see [2,19,21,28]. The study of linear operators plays an important and vital role in the field of geometric function theory.…”

Class of Analytic Functions Defined by q-Integral Operator in a Symmetric Region

“…By taking q → 1 − , the operator defined in (6) coincides with the Noor integral operator defined in [27,28]. For some details about the q-analogues of various differential operators, see [29][30][31][32][33]. The main aim of the current paper is to study the q-Noor integral operator by defining a class of analytic functions.…”