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 \(A(1/2)=1.1405\).
