Some univalence conditions related to a general integral operator-Reference-Cited by-同舟云学术

Some univalence conditions related to a general integral operator

Published:2020-12-01 Issue:2 Volume:28 Page:33-47
ISSN:1584-3289
Container-title:General Mathematics
language:en
Short-container-title:

Author:

Bărbatu Camelia¹,Breaz Daniel²

Affiliation:

1. Babeş-Bolyai University , Faculty of Mathematics and Computer Sciences, Department of Mathematics , 1, Kogălniceanu Street, 400084 Cluj-Napoca , Romania

2. 1 Decembrie University , Faculty of Science, Department of Mathematics , 5, Gabriel Bethlen Street, 510009 Alba-Iulia , Romania

Abstract

Abstract For some classes of analytic functions f, g, h and k in the open unit disk 𝕌, we consider the general integral operator 𝒢 n , that was introduced in a recent work [1] and we obtain new conditions of univalence for this integral operator. The key tools in the proofs of our results are the Pascu’s and the Pescar’s univalence criteria, as well as the Mocanu’s and Şerb’s Lemma. Some corollaries of the main results are also considered. Relevant connections of the results presented here with various other known results are briefly indicated.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/gm-2020-0013

Reference25 articles.

1. [1] C. Bărbatu, D. Breaz, Univalence Criteria for a General Integral Operator, Advancements in Complex Analysis - From Theory to Practice, to appear.

2. [2] J. Becker, Lëownersche Differentialgleichung und quasikonform fortsezbare schlichte Funktionen, J. Reine Angew. Math., vol. 255, 1972, 23-43.10.1515/crll.1972.255.23

3. [3] D. Breaz, N. Breaz, Two Integral Operators, Studia Univ.”Babes-Bolyai”, Cluj-Napoca, Mathematica, vol. 47, no. 3, 2002, 13-21.

4. [4] D. Breaz, S. Owa, N. Breaz, A new integral univalent operator, Acta Universitatis Apulensis, vol. 16, 2008.

5. [5] R. Bucur, D. Breaz, Univalence conditions for a new general integral operator, Int. Elect. J. of Pure and Applied Math., vol. 9, no. 3, 2015, 215-223.