<abstract xmlns="http://www.w3.org/1999/xhtml"><p>For some classes of analytic functions <italic>f</italic>, <italic>g</italic>, <italic>h</italic> and <italic>k</italic> in the open unit disk 𝕌, we consider the general integral operator 𝒢<italic><sub>n</sub></italic>, 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.</p></abstract>

For some classes of analytic functions f, g, h and k in the open unit disk 𝕌, we consider the general integral operator 𝒢n, 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.

Some univalence conditions related to a general integral operator

Faculty of Mathematics and Computer Sciences, Department of Mathematics

Faculty of Science, Department of Mathematics

General Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Some univalence conditions related to a general integral operator"}

For some classes of analytic functions f, g, h and k in the open unit disk 𝕌, we consider the general integral operator 𝒢n, that was introduced in a recent...

Some univalence conditions related to a general integral operator

Published Online: Dec 31, 2020

Page range: 33 - 47

Received: Apr 15, 2020

Accepted: Sep 06, 2020

DOI: https://doi.org/10.2478/gm-2020-0013

Keywords
Integral operators, analytic and univalent functions, open unit disk, univalence conditions, Schwarz Lemma

© 2020 Camelia Bărbatu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Some univalence conditions related to a general integral operator

Published Online: Dec 31, 2020

Page range: 33 - 47

Received: Apr 15, 2020

Accepted: Sep 06, 2020

DOI: https://doi.org/10.2478/gm-2020-0013

KeywordsIntegral operators, analytic and univalent functions, open unit disk, univalence conditions, Schwarz Lemma

© 2020 Camelia Bărbatu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Integral operators, analytic and univalent functions, open unit disk, univalence conditions, Schwarz Lemma