New subfamily of meromorphic multivalent starlike functions in circular domain involving _q- differential operator

Abstract

The main object of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of meromorphic multivalent starlike functions, which are defined here by means of a newly defined q-linear differential operator.

Convolution properties for a family of analytic functions involvingq-analogue of Ruscheweyh differential operator

“…Recently in 2014, Kanas and Răducanu [15] defined q -analogue of Ruscheweyh differential operator using the ideas of convolution and then studied some of its properties. For the recent extension of different operator in q -analogue, see [2,[7][8][9]16]. The aim of the current paper is to discuss some useful convolution properties for a family of analytic functions associated with circular domain involving q -analogue of Ruscheweyh differential operator.…”

A Study of Multivalent q-starlike Functions Connected with Circular Domain

“…Now when q → 1 − , the operator defined in (1.6) becomes to the familiar differential operator investigated in [12] and further, setting p = 1, we get the most familiar operator known as Ruscheweyh operator [24] (see also [3,22]). Also, for different types of operators in q-analogue, see the works [2,4,6,7,9,21].…”

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions

“…Recently, new thoughts by Maslina in [17] were used to create a novel differential operator called generalized q-differential operator with the help of q-hypergeometric functions where the authors conducted an in-depth study of applications of this operator. For further information on the extensions of different operators in q-analog, we direct the readers to [18][19][20][21][22]. The aim of the present article is to introduce a new integral operator in q-analog for multivalent functions using Hadamard product and then study some of its useful applications.…”