关键词: 超几何函数, 凸函数, 星型函数, 预星象函数, 哈达玛乘积

Abstract: Let A be the set of functions analytic in the unit disk D={z:|z|<1}. Let S^*(α) denote the class of all starlike functions of order α. Let R_α denote the set of all functions prestarlike of order α (0 ≤ α ≤ 1). Also, let R(α, β) denote the set of all functions f∈A satisfying the conditions f(0)=f'(0)-1=0 and f*(z/(1-z)^2(1-α))∈S^*(β). In this article, the authors discuss the inclusion relations between R(α, β) and some convolution properties for R_α.

Key words: Hypergeometric function, Convex function, Starlike function, Prestarlike function, Hadamard product