Geometric Properties of Certain Classes of Analytic Functions with Respect to (<i>x</i>,<i>y</i>)-Symmetric Points

Abstract

In this article, the present study employs the utilization of the concepts pertaining to (x,y)-symmetrical functions, Janowski type functions, and q-calculus in order to establish a novel subclass within the open unit disk. Specifically, we delve into the examination of convolution properties, which serve as a tool for investigating and inferring adequate and equivalent conditions. Moreover, we also explore specific characteristics of the class S˜qx,y(α,β,λ), thereby further scrutinizing the convolution properties of these newly defined classes.

Keywords

• analytic functions
• (<i>x</i>,<i>y</i>)-symmetrical functions
• <i>q</i>-calculus
• Hadamard product
• (<i>ρ</i>,<i>q</i>)-neighborhood