An integral operator on the classes S*(α) and CVH(β)

Abstract

Abstract. The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order α and from the class CVH(β) and also we estimate the first two coefficients for functions obtained by this operator applied on the class CVH(β). Preliminary and definitions.We consider the class of analytic functions f (z), in the open unit disk, U = {z ∈ C : |z| < 1}, having the form:This class is denoted by A. By S we denote the class of all functions from A which are univalent in U . We denote by K(α) the class of all convex functions of order α (0 ≤ α < 1) that satisfy the inequality:2000 Mathematics Subject Classification. 30C45.