The purpose of this paper is to obtain univalence of a certain nonlinear integral transform of functions belonging to a subclass of analytic functions. We also give several interesting geometric properties of the integral transform.

Different methods have been used in studying the univalence of the integral (1) Jα,β(f)(z) = ∫ z 0 ( f ′(t) )α(f(t) t )β dt, α, β ∈ R, where f belongs to one of the known families of holomorphic and univalent functions f(z) = z + a2z + · · · in the unit disk D = {z : |z| < 1} (see [5]). In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains ...

In this paper the author introduces a general integral operator and determines conditions for the univalence of this integral operator. Also, the significant relationships and relevance with other results are also given.

In this work we consider some integral operators for analytic functions in the open unit disk and we obtain new univalence criteria for these integral operators, using Mocanu’s and Şerb’s Lemma, Pascu’s Lemma. Mathematics Subject Classification (2010): 30C45.

We derive some criteria for univalence of certain integral operators for analytic functions in the open unit disk. 1. Introduction. Let Ꮽ be the class of the functions f (z) which are analytic in the open unit disk U = {z ∈ C : |z| < 1} and f (0) = f (0) − 1 = 0.

We improve the Ozaki’s condition for univalence of convex functions of order a. The modified Nunokawa’s Lemma is the key in the argumentation and it may have a lot of applications in the solutions of the other problems. Some new conditions for starlikeness and strongly starlikeness of order alpha are also proved in this work. 2013 Elsevier Inc. All rights reserved.

Gehring and Pommerenke have shown that if the Schwarzian derivative S f of an analytic function f in the unit disk D satisfies ISf(z)] ~_ 2(1 I z [2 ) -2, then f (D) is a Jordan domain except when f (D) is the image under a M6bius transformation of an infinite parallel strip. The condition ISf(z)l <_ 2(1 lzl2) -2 is the classical sufficient condition for univalence of Nehari. In this paper we s...

In particular we shall first determine a radius of univalence for the normalized Bessel functions [7>(z)]1/" for values of v belonging to the region G defined by the inequalities 6{\v} >0, | arg »»| <7r/4. Then we shall determine the radius of univalence of the functions z1_"7,.(z) for values of v belonging to a subset of the closure of G. When v is real and positive we shall determine the exac...