Criteria of univalence for a certain integral operator

Szymon Ignaciuk, Maciej Parol

Abstract


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

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References


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

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

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

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

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

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

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

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

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DOI: http://dx.doi.org/10.17951/a.2019.73.1.27-31
Date of publication: 2019-12-19 10:33:45
Date of submission: 2019-12-17 09:49:31


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