1. bookVolume 28 (2020): Issue 2 (December 2020)
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30 Jul 2019
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access type Open Access

Some univalence conditions related to a general integral operator

Published Online: 31 Dec 2020
Page range: 33 - 47
Received: 15 Apr 2020
Accepted: 06 Sep 2020
Journal Details
License
Format
Journal
First Published
30 Jul 2019
Publication timeframe
2 times per year
Languages
English
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.

Keywords

MSC 2010

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

[2] J. Becker, Lëownersche Differentialgleichung und quasikonform fortsezbare schlichte Funktionen, J. Reine Angew. Math., vol. 255, 1972, 23-43.Search in Google Scholar

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

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

[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.Search in Google Scholar

[6] R. Bucur, L. Andrei, D. Breaz, Univalence criterion, starlikeness and convexity for a new integral operator, Proceedings of the ICTAMI, Alba Iulia, 2015, 17-26.Search in Google Scholar

[7] B. A. Frasin, Order of convexity and univalence of general integral operator, Journal of the Franklin, vol. 348, 2011, 1012-1019.Search in Google Scholar

[8] B. A. Frasin, M. Darus, On certain analytic univalent functions, Internat. J. Math. and Math. Sci., vol. 25, no. 5, 2001, 305-310.Search in Google Scholar

[9] B. A. Frasin, J. Jahangiri A new and comprehensive class of analytic functions, Analele Univ. Oradea, Fasc. Math., vol. XV, 2008, 59-62.Search in Google Scholar

[10] I. J. Kim, E. P. Merkes, On an integral of powers of a spirallike function, Kyungpook Math. J., vol. 12, no. 2, 1972, 249-253.Search in Google Scholar

[11] O. Mayer, The Functions Theory of the One Variable Complex, Acad. Ed., Bucuresti, Romania, 1981, 101-117.Search in Google Scholar

[12] P. T. Mocanu, I. Şerb, A sharp simple criterion for a subclass of starlike functions, Complex variables, vol. 32, 1997, 161-168.Search in Google Scholar

[13] Z. Nehari, Conformal Mapping, Mc Graw-Hill Book Comp., New York, 1975 (Dover Publ. Inc., 1975).Search in Google Scholar

[14] A. Oprea, D. Breaz, Univalence conditions for a general operator, Analele Ştiinţfice ale Universitaţii “Ovidius” Constanţa, vol. 23, no. 1, 2015, 213-224.Search in Google Scholar

[15] A. Oprea, D. Breaz, H.M. Srivastava, Univalence conditions for a new family of integral Operators. Filomat, Serbia, vol. 30, no. 5, 2016, 1243-1251.Search in Google Scholar

[16] H. Oversea, Integral operators of Bazilvic type, Bull. Math. Bucuresti, vol. 37, 1993, 115-125.Search in Google Scholar

[17] S. Ozaki, M. Nunokawa, The Schwarzian derivative and univalent functions, Proceedings of the American Mathematical Society, Mathematics, vol. 33, 1972, 392-394.Search in Google Scholar

[18] N. N. Pascu, An a univalence criterion II, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj Napoca, 1985, 153-154.Search in Google Scholar

[19] N. N. Pascu, An improvement of Becker’s univalence criterion of univalence, Proceedings of the Commemorative Session Simion Stoilov, Braşov, 1987.Search in Google Scholar

[20] N. N. Pascu, V. Pescar, On the integral operators Kim-Merkes and Pfaltzgraff, Mathematica, Univ. Babes-Bolyai, Cluj-Napoca, vol. 32, no. 2, 1990, 185-192.Search in Google Scholar

[21] V. Pescar, A new generalization of Ahlfors’s and Becker’s criterion of univalence, Bull. Malaysian Math. Soc., vol. 19, no. 2, 1996, 53-54.Search in Google Scholar

[22] Pescar V., New univalence criteria for some integral operators, Studia Univ. Babes-Bolyai Math., vol. 59, no. 2, 2014, 185-192.Search in Google Scholar

[23] V. Pescar, S. Owa, Univalence of certain integral operators, Int. J. Math. Math. Sci., vol. 23, 2000, 697-701.Search in Google Scholar

[24] J. Pfaltzgraff, Univalence of the integral of (f′ (z))λ, Bull. London Math. Soc., vol. 7, no. 3, 1975, 254-256.Search in Google Scholar

[25] N. Ularu, D. Breaz, Univalence criterion and convexity for an integral operators, Applied Mathematics Letters, vol. 25, 2012, 658-661.Search in Google Scholar

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