Abstract
For analytic functions f and g in the open unit disc 𝕌, a new general integral operator is introduced. The main objective of this paper is to obtain univalence condition and order of convexity for this general integral operator.
Highlights
Introduction and PreliminariesLet A be the class of all functions of the form ∞f (z) = z + ∑akzk, (1)k=2 which are analytic in the open unit diskU = {z ∈ C : |z| < 1} . (2) let S denote the subclass of A consisting of functions f which are univalent in U.A function f ∈ A is said to be starlike of order α (0 ≤ α < 1) if it satisfies the inequality Re {
K=2 which are analytic in the open unit disk
Let S denote the subclass of A consisting of functions f which are univalent in U
Summary
A function f ∈ A is said to be starlike of order α (0 ≤ α < 1) if it satisfies the inequality. A function f ∈ A is said to be convex of order α (0 ≤ α < 1) if it satisfies the inequality. A function f ∈ A belongs to the class R(α) (0 ≤ α < 1) if it satisfies the inequality. The family B(μ, α) (μ ≥ 0, 0 ≤ α < 1) which contains the functions f that satisfy the condition. Was studied by Frasin and Jahangiri [1]. This family is a comprehensive class of analytic functions that contains other new classes of analytic univalent functions as well as some very well-known ones.
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