Starlikeness for Analytic Function
Rahmalia Firdausi Tamara

Universitas Brawijaya

Abstract

This research discusses the sufficient conditions for the starlikeness of an analytic function. We generalized the values by adding the parameter \(\beta\) to \(A\), such that become \(A(\beta)\) for \(0<\beta\leq1\). The proof process involves the use of several lemmas, such as the Miller-Mocanu Lemma, Clunie-Jack Lemma, and combinatorics lemma. By using simple computation, we obtained \(A(0)=2.6061\), which is an improvement from Miller-Mocanu^s journal with \(A=2\) and Nunokawa-Thomas with \(A=2.5159\). In addition to \(\beta=0\), we choose \(\beta=1/2\), such that \(A(1/2)=1.1405\).

Keywords: Analytic function, starlike function, sufficient condition

Topic: Complex Analysis