Univalence Conditions for Two General Integral Operators

Adriana Oprea, Daniel Breaz

Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, Alba Iulia, Romania.
Department of Mathematics, University of Pite?ti, Pite?ti, Romania.

DOI: 10.4236/apm.2014.48054                

Abstract

Let A be the class of all analytic functions which are analytic in the open unit disc  . In this paper we study the problem of univalence for the following general integral operators:

Keywords

Analytic Functions, Integral Operators, General Schwarz Lemma

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Becker, J. (1972) Lownersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen. Journal für die Reine und Angewandte Mathematik, 255, 23-43.
[2]	Nehari, Z. (1952) Conformal Mapping. McGraw-Hill Book Company, New York.
[3]	Alexander, J.W. (1915) Functions Which Map the Interior of the Unit Circle upon Simple Regions. Annals of Mathematics, 17, 12-22. http://dx.doi.org/10.2307/2007212
[4]	Pescar, V. (1997) On Some Integral Operations Which Preserve the Univalence. Journal of Mathematics, 30, 1-10.
[5]	Pescar, V. (1998) On the Univalence of an Integral Operator. Studia Universitatis “Babes-Bolyai”, Cluj-Napoca, Mathematica, 43, 95-97.
[6]	Breaz, D. and Breaz, N. (2002) Two Integral Operators. Studia Universitatis “Babes-Bolyai”, Cluj-Napoca, Mathematica, 3, 13-21.
[7]	Breaz, D. (2008) Certain Integral Operators on the Classes M(βi) and N(βi). Journal of Inequalities and Applications, Article ID: 719354.
[8]	Pescar, V. (1997) Some Integral Operators and Their Univalence. The Journal of Analysis, 5, 157-162.
[9]	Pescar, V. (1997) An Integral Operator Which Preserves the Univalency. The Annual Conference of the Romanian Society of Mathematical Sciences, Bucharest, 29 May-1 June 1997, 179-181.
[10]	Ularu, N. and Breaz, D. (2012) Univalence Criterion and Convexity for an Integral Operator. Applied Mathematics Letter, 25, 658-661. http://dx.doi.org/10.1016/j.aml.2011.10.011
[11]	Ularu, N. and Breaz, D. (2013) Univalence Condition and Properties for Two Integral Operators. Applied Sciences, 15, 112-117.