The Choi–Saigo–Srivastava integral operator and a class of analytic functions

摘要

Let A be the class of the normalized analytic functions in the unit disk U, and K(α) denote the subclass of A consisting of the convex functions of order α in U. It is known that the operator fλ,μ was defined such that fλ ∗ fλ,μ = z/(1 − z)μ (μ > 0), where ∗ denotes the Hadamard product and fλ = z/(1 − z)λ+1 (λ > − 1). The Choi–Saigo–Srivastava integral operator Iλ,μ was defined such that Iλ,μf=fλ,μ∗f. By using the operator Iλ,μ, we define the class K(λ,μ)(α)={f∈A∣Iλ,μf∈K(α)}. In this paper, we study various inclusion properties of this class, some distortion theorems and coefficient inequalities. We have also provided some well-known results as corollaries of our theorems.