Applications of <i>q</i>-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

Abstract

In this article, a new linear extended multiplier operator is defined utilizing the q-Choi–Saigo–Srivastava operator and the q-derivative. Two generalized subclasses of q—uniformly convex and starlike functions of order δ—are defined and studied using this new operator. Necessary conditions are derived for functions to belong in each of the two subclasses, and subordination theorems involving the Hadamard product of such particular functions are stated and proven. As applications of those findings using specific values for the parameters of the new subclasses, associated corollaries are provided. Additionally, examples are created to demonstrate the conclusions’ applicability in relation to the functions from the newly introduced subclasses.

Keywords

• subordination
• uniformly starlike function
• uniformly convex function
• convolution (Hadamard) product
• subordinating factor sequence
• <i>q</i>-derivative operator