Generalized radius problems for quotient functions having fixed second coefficient

TL;DR

This paper investigates radius problems for specific classes of quotient functions with fixed second coefficients, providing new estimates for various starlikeness types and relating them to existing results.

Contribution

It introduces new radius estimates for quotient functions with fixed second coefficients across multiple starlikeness classes, expanding the understanding of their geometric properties.

Findings

Derived radius estimates for strongly starlike and lemniscate starlike functions.

Established relations between new and existing radius estimates.

Analyzed various starlikeness conditions for quotient functions.

Abstract

In this manuscript, we deal with three classes of quotient functions having fixed second coefficient described on open unit disk. The radius of strongly starlikeness, lemniscate starlikeness, lune starlikeness, parabolic starlikeness, sine starlikeness, exponential starlikeness and several other radius estimates for such classes are examined. Relevant relations of obtained radius estimates with the existing estimates are also discussed.