Some sufficient problems for certain univalent functions

TL;DR

This paper investigates sufficient conditions under which certain classes of analytic functions in the unit disk are univalent, extending previous work on analytic functions with specific normalization.

Contribution

It introduces new sufficient conditions for functions to belong to specific classes of univalent functions, broadening the understanding of univalence criteria.

Findings

Established new sufficient conditions for univalence.

Extended previous results to broader classes of functions.

Provided theoretical criteria for analytic functions in the unit disk.

Abstract

For analytic functions f(z) in the open unit disk U with f(0)=f'(0)-1=0, R. Singh and S. Singh (Coll. Math. 47(1982), 309-314) have considered some sufficient problems for f(z) to be univalent in U. The object of the present paper is to discuss some sufficient problems for f(z) to be some classes of analytic functions in U.