On the univalence of two general integral operators

Abstract

In this paper, we define two new general integral operators in the unit disc U. The main object of this paper is to give sufficient conditions for these integral operators, which are defined here by means of the normalized form of univalent functions and belongs to some special subclasses of its, to be univalent in the open unit disk U.

Univalence conditions for an integral operator defined by a generalization of the Srivastava-Attiya operator

“…Our main results are contained in Theorems 1, 2 and 3. By suitably specializing these main results, we have deduced several corollaries and consequences which were derived in a number related earlier works on the subject of investigation here (see also the recent works [9], [10], [11] and [23]).…”

Sufficient conditions for univalence - Univalence of Certain Integral Operators Involving Generalized Struve functions

“…Frasin [18] and Arif and Raza [2] studied the convexity and strongly convexity of the integral operators dened in [4]. Recently Deniz et al [16] and Deniz [10] studied the integral operator dened by generalized Bessel functions of order v. For further details of these univalence criterion, we refer the readers to [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,25,26,27,28]. Motivated by the work of these above authors, we contribute to this univalence theory by studying the univalence of integral operators involving generalized Struve functions.…”

A Subclass of Noor-Type Harmonic p-Valent Functions Based on Hypergeometric Functions

“…In 1915, Alexander [4] introduced the first integral operator on class A that includes normalized regular functions. Later, several well-known integral operators are investigated by complex analysts, such as Libera [26], Bernardi [9], Miller, Mocanu and Reade [27,28], Pascu and Pescar [34], Ong et al [33], Frasin [20], Frasin and Breaz [21], El-Ashwah, Aouf and El-Deeb [16], Deniz [13], Rahrovi [35], Al-Janaby and Ghanim [5], Al-Janaby, Ghanim, Darus [6], Al-Janaby [7] and others. The following are some important linear operators related to results in this study.…”