Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Abstract

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series

“…In lights of (36), thus it completes the proof of inequality in (32). Moreover, to find the inequality (33), we set:…”

“…Motivated by a recently published article by Shi et al [30], in which they have found estimates for some coefficient functionals for three leaf-type starlike functions, from [31] where coefficient bounds for certain subclasses of analytic functions connected with Faber polynomial have been derived, and some other related works on this subject (see for example [32][33][34][35]). We will now define the following concepts:…”

Certain New Subclass of Multivalent Q-Starlike Functions Associated with Q-Symmetric Calculus

“…Subsequently, a number of q-analogue operators have been defined. More in-depth information about operators in q-calculus, is available in [5][6][7][8][9]. In [10,11], Arif et al defined and investigated some new subclasses of multivalent functions by implementing the concept of the q-derivative operator, while Zang et al [12] used the basic concepts of q-calculus to define the generalized conic domain.…”

Applications of Borel-Type Distributions Series to a Class of Janowski-Type Analytic Functions

“…It is observed that this formalism makes further mathematical exploration easier, and also improves the understanding of the geometric and symmetric properties of such operators. The importance of convolution in the theory of operators may easily be understood from the work in [7][8][9][10]. Furthermore, probability is not just about flipping coins and counting cards in a disc; it is used in a wide range of real-life areas, from insurance to meteorology and politics to economics forecasting.…”