Radius and Convolution problems of analytic functions involving Semigroup Generators

TL;DR

This paper investigates the criteria for normalized analytic functions to be infinitesimal generators using Hadamard products, explores their subclasses, and addresses radius problems, extending existing results in the field.

Contribution

It introduces new membership criteria and generalizes known results for classes of infinitesimal generators and their subclasses using Hadamard product techniques.

Findings

Established Hadamard product criteria for infinitesimal generators

Analyzed embedding of subclasses of univalent functions

Solved radius problems for the class of infinitesimal generators

Abstract

We establish the membership criteria in terms of Hadamard product for a normalized analytic function to be in the class of infinitesimal generators. Furthermore, the embedding of various subclasses of normalized univalent functions in the class of infinitesimal generators and the radii problems for this class are studied. The results derived, generalize the already known results.