Subordinateness of the subclass of Bazilevic functions B_2(α)

Marjono
Gaspar, Estelita Maria Fernandes
Tamara, Rahmalia Firdausi

Hilbert Journal of Mathematical Analysis
Vol. 1 No. 2 (2023): Hilbert J. Math. Anal.

In 1999 Marjono has published about the subordinateness of subclass of Bazilevic functions. However, the value of β(γ) is not the largest one. In this paper we present our work with my student Estelita Maria from Universidade Timor Loro Sa’e and Rahmalia Firdausi Tamara to find the largest β(γ). This result was obtain by using the similar way with the theorem before and stressing in optimize approaching and also by using the maximum modulus principles as mention in Remark 1.9. For an analytic, normalized function f such that f(0) = f′(0)−1 = 0, there is a largest number β∗(γ) such that subordination holds for α > 0, 0 < γ ≤ 1 and z ∈ D as an improvement of Marjono’s work.