On A Special Type Of Ma-Minda Function

TL;DR

This paper introduces a new special type of Ma-Minda function, explores its properties, and applies it to subclasses of starlike functions, establishing inclusion, radius, and coefficient bounds, thus generalizing previous results.

Contribution

It defines a novel class of Ma-Minda functions with unique conditions and studies their properties, including coefficient bounds and applications to starlike functions.

Findings

Established inclusion and radius results for the new class.

Derived bounds for the fourth coefficient and second Hankel determinant.

Generalized many earlier known results through convolution techniques.

Abstract

This paper deals with a special type of Ma-Minda function introduced here with many fascinating facts and interesting applications. It is much akin in all aspects but differs by a condition from its Ma-Minda counterpart. Further, we consider the function:~$1-\log(1+z)$, a special Ma-Minda of the type introduced here, to define a subclass of starlike functions in a similar fashion as we do with Ma-Minda function and is studied for establishing inclusion and radius results. Apart from that, we also deal with the majorization and Bloch function norm problems for the same class. In addition, we obtain the bounds of fourth coefficient:~$a_4$ and second Hankel determinant:~$H_2(2)$ for the functions belonging to a newly defined class using convolution, which generalizes many earlier known results and its association with the special type of Ma-Minda function is also pointed out.