Second-order differential subordinations for analytic functions with fixed initial coefficient

TL;DR

This paper introduces a new methodology for second-order differential subordination tailored to analytic functions with fixed initial coefficients, enhancing understanding of convex and starlike functions with fixed second coefficients.

Contribution

It develops a novel approach to second-order differential subordination for functions with fixed initial coefficients, extending existing theories and applications.

Findings

New methodology for second-order differential subordination.

Applications to convex and starlike functions with fixed second coefficient.

Several illustrative examples provided.

Abstract

Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several interesting examples are given. The results obtained are applied to the classes of convex and starlike functions with fixed second coefficient.