On the successive coefficients of certain univalent functions

TL;DR

This paper investigates the relationships between successive coefficients of specific subclasses of univalent functions, providing sharp results and a new proof for Robertson's conjecture on close-to-convex functions.

Contribution

It introduces new sharp coefficient inequalities for subclasses of univalent functions and offers a concise proof of Robertson's conjecture.

Findings

Established sharp coefficient inequalities for certain univalent function subclasses.

Provided a new, concise proof of Robertson's conjecture.

Enhanced understanding of coefficient relationships in univalent function theory.

Abstract

The object of this paper is to study relationship between successive coefficients of some subclasses of the class of univalent functions in the unit disk. the result obtained is sharp, and is used to provide a new, short proof of the well-known conjecture of Robertson on the coefficients of close-to-convex functions.