Geodesic
Criteria of univalence for a certain integral operator
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 73 (2019) no. 1.

Voir la notice de l'article provenant de la source Library of Science

In this article we consider the problem of univalence of a function introduced by Breaz and Ularu, improve some of their results and receive not only univalence conditions but also close-to-convex conditions for this function. To this aim, we used our method based on Kaplan classes.
Keywords: Univalence, integral operators, Kaplan classes 
@article{AUM_2019_73_1_a4,
     author = {Ignaciuk, Szymon and Parol, Maciej},
     title = {Criteria of univalence for a certain integral operator},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {73},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a4/}
}
TY  - JOUR
AU  - Ignaciuk, Szymon
AU  - Parol, Maciej
TI  - Criteria of univalence for a certain integral operator
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2019
VL  - 73
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a4/
LA  - en
ID  - AUM_2019_73_1_a4
ER  - 
%0 Journal Article
%A Ignaciuk, Szymon
%A Parol, Maciej
%T Criteria of univalence for a certain integral operator
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2019
%V 73
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a4/
%G en
%F AUM_2019_73_1_a4
Ignaciuk, Szymon; Parol, Maciej. Criteria of univalence for a certain integral operator. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 73 (2019) no. 1. http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a4/

[1] Biernacki, M., Sur l’integrale des fonctions univalentes, Bull. Pol. Acad. Sci. 8 (1960), 29–34.

[2] Breaz, D., Ularu, N., Univalence criterion and convexity for an integral operator, Appl. Math. Letters 25 (3) (2012), 658–661.

[3] Causey, W. M., The univalence of an integral, Proc. Amer. Math. Soc. 3 (1971), 500–502.

[4] Godula, J., On univalence of a certain integral, Ann. Univ. Mariae Curie-Skłodowska Sect. A 33 (1979), 69–76.

[5] Ignaciuk, S., Parol, M., Kaplan classes and their applications in determining univalence of certain integral operators, 2018 (to appear).

[6] Krzyż, J., Lewandowski, Z., On the integral of univalent functions, Bull. Pol. Acad. Sci. 7 (1963), 447–448.

[7] Merkes, E. P., Wright, D. J., On the univalence of a certain integral, Proc. Amer. Math. Soc. 27 (1971), 97–100.

[8] Pfaltzgraf, J. A., Univalence of an integral, Proc. Amer. Math. Soc. 3 (1971), 500–502.

[9] Ruscheweyh, S., Convolutions in Geometric Function Theory, Seminaire de Math. Sup. 83, Presses de l’Universite de Montreal, 1982.