Some univalence conditions related to a general integral operator

Camelia Bărbatu; Daniel Breaz

doi:10.2478/gm-2020-0013

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Some univalence conditions related to a general integral operator

General Mathematics

Volume 28 (2020): Issue 2 (December 2020)

By: Camelia Bărbatu and Daniel Breaz

Open Access

|Dec 2020

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/gm-2020-0013 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

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Language: English

Page range: 33 - 47

Submitted on: Apr 15, 2020

Accepted on: Sep 6, 2020

Published online: Dec 31, 2020

Published in print: Dec 1, 2020

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Keywords:

Integral operators,

analytic and univalent functions,

open unit disk,

univalence conditions,

Schwarz Lemma

MSC:

30C45,

30C75

Related subjects:

Mathematics,

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2020 Camelia Bărbatu, Daniel Breaz, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 28 (2020): Issue 2 (December 2020)