Some sufficient problems for strongly close-to-convex of order \mu

TL;DR

This paper investigates sufficient conditions under which certain analytic functions in the unit disk are strongly close-to-convex of a specified order, contributing to geometric function theory.

Contribution

It introduces new sufficient conditions for functions to be strongly close-to-convex of order rac{(z)}{(z)} in the unit disk.

Findings

Established new criteria for strong close-to-convexity of order rac{(z)}{(z)}.

Extended understanding of geometric properties of analytic functions.

Provided theoretical results without empirical validation.

Abstract

For analytic functions f(z) in the open unit disk U with f(0)=f'(0)-1=0, a class STC(\mu) is defined. The object of the present paper is to discuss some sufficient problems for f(z) to be strongly close-to-convex of order \mu\ in U.