Univalence Criteria for a General Integral Operator

Bărbatu, Camelia; Breaz, Daniel

doi:10.2478/gm-2019-0014

Abstract

In this paper we introduce a new general integral operator for analytic functions in the open unit disk 𝕌 and we obtain sufficient conditions for univalence of this integral operator.

References

[1] C. L. Aldea, V. Pescar, Univalence Criteria for a general integral operator, Transilvania University of Brasov, vol. 10, no. 2, 2017, 19-30.
Search in Google Scholar Back to article
[2] 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 Back to article
[3] D. Breaz, N. Breaz, H. M. Srivastava, An extension of the univalent condition for a family of integral operators, Appl. Math. Lett., vol. 22, no. 3, 2009, 41-44.10.1016/j.aml.2007.11.008
Search in Google Scholar Back to article
[4] D. Breaz, S. Owa, N. Breaz, A new integral univalent operator, Acta Universitatis Apulensis, vol. 16, 2008.
Search in Google Scholar Back to article
[5] B. A. Frasin, Order of convexity and univalence of general integral operator, Journal of the Franklin, vol. 348, 2011, 1012-1019.10.1016/j.jfranklin.2011.03.006
Search in Google Scholar Back to article
[6] B. A. Frasin, Sufficient conditions for the univalence of an integral operator, Asia Pacific Journal of Mathematics, vol.5, no.1, 2018, 85-91.
Search in Google Scholar Back to article
[7] 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 Back to article
[8] O. Mayer, The Functions Theory of the One Variable Complex, Acad. Ed., Bucuresti, Romania, 1981, 101-117.
Search in Google Scholar Back to article
[9] H. Oversea, Integral operators of Bazilvic type, Bull. Math. Bucuresti, vol. 37, 1993, 115-125.
Search in Google Scholar Back to article
[10] S. Ozaki, M. Nunokawa, The Schwarzian derivative and univalent functions, Proceedings of the American Mathematical Society, Mathematics, vol. 33, 1972, 392-394.10.1090/S0002-9939-1972-0299773-3
Search in Google Scholar Back to article
[11] N. N. Pascu, An improvement of Beker’s univalence criterion, Proceedings of the Commemorative Session Simion Stoilov, University of Braso, 1987, 43-48.
Search in Google Scholar Back to article
[12] N. N. Pascu, V. Pescar, On the integral operators Kim-Merkes and Pfaltzgra, Mathematica, UBB, Cluj-Napoca, vol. 32, no. 2, 1990, 185-192.
Search in Google Scholar Back to article
[13] V. Pescar, New univalence criteria for some integral operators, Studia Univ.”Babes-Bolyai”, Cluj-Napoca, Mathematica, vol. 59, no. 2, 2014, 185-192.
Search in Google Scholar Back to article
[14] V. Pescar, A new generalization of Ahlfors’s and Becker’s criterion of univalence, Bulletin of Malaysian Mathematical Society, vol. 19, no.2, 1996, 53-54.
Search in Google Scholar Back to article
[15] V. Pescar, Univalence criteria of certain integral operators, Acta Ciencia Indica, Mathematics, vol. 29, no. 1, 2003, 135-138.
Search in Google Scholar Back to article
[16] V. Pescar, On the univalence of some integral operators, General Mathematics, vol. 14, no. 2, 2006, 77-84.
Search in Google Scholar Back to article
[17] V. Pescar, S. Owa, Univalence of certain integral operators, Int. J. Math. Math. Sci., vol. 23, 2000, 697-701.10.1155/S016117120000260X
Search in Google Scholar Back to article
[18] J. Pfaltzgraff, Univalence of the integral of (f′ (z))^λ, Bull. London Math. Soc., vol. 7, no. 3, 1975, 254-256.10.1112/blms/7.3.254
Search in Google Scholar Back to article
[19] L. Stanciu, The Univalence conditions of some integral operators, Abstract and Applied Analysis, ID 924645, 2012, 9 pages.10.1155/2012/924645
Search in Google Scholar Back to article
[20] L. F. Stanciu, D. Breaz, H. M. Srivastava, Some criteria for univalence of a certain integral operator, Novi Sad J. Math. vol. 43, no. 2, 2013, 51-57.
Search in Google Scholar Back to article
[21] P. T. Mocanu, T. Bulboaca, G. S. Salagean, Teoria geometrica a functiilor univalente, Casa Cartii de Stiinta, Cluj Napoca, 1999, 77-81.
Search in Google Scholar Back to article

Univalence Criteria for a General Integral Operator

Abstract

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