Starlikeness of order \alpha\ rerated to Mocanu functions

TL;DR

This paper investigates conditions under which Mocanu functions, analytic in the unit disk and satisfying certain initial conditions, are starlike of a given order, extending understanding of their geometric properties.

Contribution

It provides new sufficient conditions for Mocanu functions to be starlike of order alpha, advancing the geometric function theory related to these functions.

Findings

Established new sufficient conditions for starlikeness of Mocanu functions.

Extended the class of functions known to be starlike of a certain order.

Contributed to the geometric analysis of 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, P. T. Mocanu (Mathematica (Cluj), 11(34) (1969)) have considered Mocanu functions. The object of the present paper is to discuss some sufficient problems for f(z) to be starlike of order \alpha.