Univalence Conditions for Two General Integral Operators

DOI: 10.4236/apm.2014.48054   PDF   HTML     3,893 Downloads   4,348 Views   Citations

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:


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Oprea, A. and Breaz, D. (2014) Univalence Conditions for Two General Integral Operators. Advances in Pure Mathematics, 4, 487-493. doi: 10.4236/apm.2014.48054.

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.

  
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