The General Subclasses of the Analytic Functions and Their Various Properties

TL;DR

This paper introduces two new subclasses of analytic functions, explores their properties, and provides necessary and sufficient conditions for membership, expanding the theoretical framework of analytic function subclasses.

Contribution

The paper defines and investigates two new general subclasses of analytic functions, providing comprehensive conditions for their characterization.

Findings

Defined new subclasses $S^*C(α,β;γ)$ and $TS^*C(α,β;γ)$

Established necessary and sufficient conditions for class membership

Enhanced understanding of properties of analytic function subclasses

Abstract

The object of the present paper is to introduce and investigate two new general subclasses ${{S}^{*}}C(\alpha ,\beta ;\gamma )$ and $T{{S}^{*}}C(\alpha ,\beta ;\gamma )~~(\alpha, \beta \in [0,1),~\gamma \in [0,1])$ of the analytic functions. Here, we give sufficient conditions as well as necessary and sufficient conditions for the functions belonging to the classes.