On a Generalized Integral Operator

Affiliation(s)

Department of Mathematics, University of Pitesti, Arge?, Romania.

Department of Mathematics, University “1st December 1918” of Alba Iulia, Alba Iulia, Romania.

Department of Mathematics, “Lucian Blaga” University of Sibiu, Sibiu, Romania.

Department of Mathematics, University of Pitesti, Arge?, Romania.

Department of Mathematics, University “1st December 1918” of Alba Iulia, Alba Iulia, Romania.

Department of Mathematics, “Lucian Blaga” University of Sibiu, Sibiu, Romania.

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*I*^{1}(*z*), in Section 3 of this paper.

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

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.

Dorca, I. , Breaz, D. and Acu, M. (2013) On a Generalized Integral Operator.

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

[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