Univalence criteria for certain integral operator

In this paper we introduce a new general integral operator for analytic functions in the open unit disk U in the complex plane as an extension of the integral operator defined by P. Dicu, M. Dicu and A.F. Albisoru. We focus our attention on some sufficient conditions for the univalence of the integral operator. We end this paper with a remark on a modification of the studied integral operator.

analytic function, univalence, integral operator

[1] Barbatu C., Breaz D., Univalence criteria for a general integral operator, General Mathematics, 27 (2019), no. 2, 43–57.
[2] Blezu D., Pascu R.N., Univalence criteria for integral operators, Glasnik Matematicki, 36(56) (2001), no. 2, 241–245.
[3] Bucur R., Andrei L., Breaz D., Properties of a new integral operator, An. St. Univ. Ovidius Constant¸a, 24(2) (2016), 127–136.
[4] Dicu P., Dicu M., Albisoru A.F., On some univalence criteria for certain integral operators, Stud. Univ. Babes-Bolyai Math 70 (2025), no. 4, 585–596 (DOI: 10.24193/subbmath.2025.4.04)
[5] Duren P.L., Univalent Functions, Springer Verlag, New York, 1983.
[6] Frasin B.A., Univalence criteria for general integral operator, Math. Commun., 16 (2011), 115–124.
[7] Goodman A.W., Univalent Functions, Mariner Publ. Comp., Tampa, Florida,1984.
[8] Graham I., Kohr G., Geometric Function Theory in One and Higher Dimensions, Marcel Deker Inc., New York, 2003.

[9] Kohr G., Mocanu P.T., Special Chapters of Complex Analysis (in romanian), Cluj University Press, Cluj-Napoca, 2005.
[10] Liu J., Yang D., On a class of univalent functions, Internat. J. Math. and Math. Sci. 22(3) (1990), 605–610.
[11] Mocanu P.T., Bulboaca T., Salagean G.S¸., Geometric theory of univalent functions (in romanian), Casa Cartii de Stiinta, Cluj-Napoca, 2006.
[12] Pascu N.N., An improvement of Becker’s univalence criterion, University of Brasov, Department of Mathematics, Procedings of the commemorative session Simion Stoilov (1987), 43–48.
[13] Pescar V., Univalence of certain integral operators, Acta Universitatis Apulensis, 12 (2006), 43–48.
[14] Pescar V., On the univalence of some integral operators, General Mathematics, 14 (2006), no. 2, 77–84.
[15] Pescar V., On some integral operators which preserve the univalence, Stud. Univ. Babes-Bolyai Math. 33 (2008), no. 1, 57–61.
[16] Pescar V., New univalence criteria for some integral operators, Stud. Univ. Babes-Bolyai Math. 59 (2014), no. 2, 167–176.
[17] Stanciu L, The univalence conditions of some integral operators, Abstr. Appl. Anal., art. no. 924645 (2012), 9 pp.

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P. Dicu, M. Dicu, E.S. Grigoriciuc, Univalence criteria for certain integral operator, Bull. Transilv. Univ. Brasov, Ser. III, Math. Comput. Sci. (2026), to appear

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