Radii Constants for Functions with Fixed Second Coefficient

TL;DR

This paper introduces three classes of analytic functions with fixed second coefficients, determines their radii within starlike subclasses, and improves upon previous radius estimates with connections to earlier results.

Contribution

It defines new classes of functions with fixed second coefficients and provides improved radius estimates for their inclusion in starlike subclasses.

Findings

New radius estimates are better than previous results.

Connections established with known results.

Enhanced understanding of functions with fixed second coefficients.

Abstract

We introduce three classes of analytic functions with fixed second coefficient which are defined using the class $\mathcal{P}$ of analytic functions with positive real part. The objective is to determine radii such that the three classes are contained in various subclasses of starlike functions. The radii estimated in the present investigation are better than the radii obtained earlier. Furthermore, connections with previous known results are shown.