On some $n$-starlike integral operators

TL;DR

This paper proves that certain generalized integral operators preserve $n$-starlikeness in the unit disk, extending and improving upon previous results in geometric function theory.

Contribution

It completes a lemma of Babalola and Opoola and demonstrates that these operators maintain $n$-starlikeness, broadening the scope of known preservation results.

Findings

Generalized integral operators preserve $n$-starlikeness in the unit disk.

The results extend and improve previous theorems in the field.

The paper completes a key lemma to establish these properties.

Abstract

By a completion of a lemma of Babalola and Opoola \cite{KT}, we prove that certain generalized integral operators preserve $n$-starlikeness in the open unit disk $E=\{z\in \mathbb{C}: |z|<1\}$. Our results generalize, extend and improve many known ones.