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On a Generalized Integral Operator

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DOI: 10.4236/am.2013.411214    3,274 Downloads   4,561 Views  

ABSTRACT

We have considered several integral operators from literature and we have made a generalization of them. It can be easily seen that their properties are also preserved. Therefore, we use known results concerning the starlike functions (see [1,2]) and we unify some known integral operators (see [3]) into one single integral operator, called I1(z), in Section 3 of this paper.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Dorca, I. , Breaz, D. and Acu, M. (2013) On a Generalized Integral Operator. Applied Mathematics, 4, 1590-1594. doi: 10.4236/am.2013.411214.

References

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[2] M. Acu and S. Owa, “Note on a Class of Starlike Functions,” Proceeding of the International Short Joint Work on Study on Calculus Operators in Univalent Function Theory, Kyoto, 2006, pp. 1-10.
[3] D. Breaz, “Integral Operators on Univalent Function Spaces,” Academiei Romane, Bucuresti, 2004.
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[5] M. Darus and R. W. Ibrahim, “Generalized Cesáro Integral Operator,” International Journal of Pure and Applied Mathematics, Vol. 69, No. 4, 2011, pp. 421-427.
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[7] I. Dorca, D. Breaz and M. Acu, “Mapping Properties of Some Classes of Analytic Functions under Generalized Integral Operators,” Advances in Mathematics: Scientific Journal, Vol. 1, No. 1, 2012, pp. 51-57.
[8] I. Dorca, M. Acu and D. Breaz, “Note on Neighborhoods of Some Classes of Analytic Functions with Negative Coefficients,” ISRN Mathematical Analysis, 2011, Article ID: 610549.
[9] I. Dorca, D. Breaz and M. Acu, “Subordonation of Certain Subclass of Convex Function,” Studia Universitatis Babes-Bolyai, Vol. 57, No. 2, 2012, pp. 181-187.
[10] G. S. Salagean, “Geometria Planului Complex,” Promedia Plus, Cluj-Napoca, 1999.
[11] H. Silverman, “Univalent Functions with Negative Coefficients,” Proceedings of the American Mathematical Society, Vol. 5, 1975, pp. 109-116.
http://dx.doi.org/10.1090/S0002-9939-1975-0369678-0

  
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