Applications of Theory of Differential Subordination for Functions with Fixed Initial Coefficient to Univalent Functions

TL;DR

This paper applies the theory of differential subordination to univalent functions with fixed initial coefficients, improving existing results by emphasizing the role of the second coefficient in these functions.

Contribution

It introduces new results for subclasses of univalent functions with fixed second coefficients using differential subordination techniques.

Findings

Enhanced bounds for subclasses of univalent functions.

Clear influence of the second coefficient on function properties.

Improved results compared to classical univalent function theory.

Abstract

By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions is evident in the results obtained.