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 convex functions, which are defined here by means of a newly defined q-linear differential operator.
Highlights
Introduction and DefinitionsQuantum calculus (q-calculus), which is the study of classical calculus without the notion of limits, attracted the researchers because of its applications in various branches of mathematics, physics and various other branches of science, for details see [6, 7].The q-analogue of derivative and integral operators were introduced by Jackson [13, 14] along with some applications of q-calculus
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 convex functions, which are defined here by means of a newly defined q-linear differential operator
Kanas and Raducanu [15] gave the q-analogue of Ruscheweyh differential operator using the concepts of convolution and studied some of its properties
Summary
Introduction and DefinitionsQuantum calculus (q-calculus), which is the study of classical calculus without the notion of limits, attracted the researchers because of its applications in various branches of mathematics, physics and various other branches of science, for details see [6, 7].The q-analogue of derivative and integral operators were introduced by Jackson [13, 14] along with some applications of q-calculus. Kanas and Raducanu [15] gave the q-analogue of Ruscheweyh differential operator using the concepts of convolution and studied some of its properties. In this paper a q-differential operator for meromorphic functions using convolution is defined. We use this operator to define and study some properties of a family of meromorphic convex functions associated with circular domain.
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