AM  Vol.4 No.11 , November 2013
On a Generalized Integral Operator
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.

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
[1]   M. Acu, I. Dorca and S. Owa, “On Some Starlike Functions with Negative Coefficients,” Proceedings of the International Conference on Theory and Applications of Mathematics and Informatics, Alba Iulia, 21-24 July 2011, pp. 101-112.

[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.

[4]   D. Breaz, H. O. Güney and G. S. Salagean, “A New General Integral Operator,” Tamsui Oxford Journal of Mathematical Sciences, Vol. 25, No. 4, 2009, pp. 407-414.

[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.

[6]   I. Rahovean (Dorca) and A. I. Rahovean, “New Integral Operators—Properties,” LAP Publishing, Saarbrücken, 2013.

[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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