Geometric Properties of a Class of Analytic Functions Defined by a Differential Inequality

Abstract

Let A be the class of analytic functions f defined in the open unit disk E and normalized by f(0)=f'(0)-1=0. For f(z)/z≠0 in E, let Mα,λ:={f∈A:|-αz2(z/f(z))′′  +f′(z)(z/f(z))2-1|≤λ,  z∈E}, where λ>0 and α∈R∖[-1/2,0]. In the present paper, we find conditions under which functions in the class M(α,λ) are starlike of order γ, 0≤γ<1.