Generalization of Certain Subclasses of Multivalent Functions with Negative Coefficients Defined by Cho-Kwon-Srivastava Operator
Elsayed A. Elrifai, Hanan E. Darwish, Abdusalam R. Ahmed
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DOI: 10.4236/am.2011.210171   PDF    HTML     4,742 Downloads   8,377 Views  

Abstract

Making use of the Cho-Kwon-Srivastava operator, we introduce and study a certain SCn (j, p, λ, α, δ) of p-valently analytic functions with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorem, radii of close-to-convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class SCn (j, p, λ, α, δ). Finally, several applications investigate an integral operator, and certain fractional calculus operators also considered.

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E. Elrifai, H. Darwish and A. Ahmed, "Generalization of Certain Subclasses of Multivalent Functions with Negative Coefficients Defined by Cho-Kwon-Srivastava Operator," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1225-1235. doi: 10.4236/am.2011.210171.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] P. L. Duren, “Univalent functions,” In: Grundlehen der Mathematischen Wissenschaften, Vol. 259, Springer- Verlag, New York, 1983.
[2] A. W. Goodman, “Univalent Functions, Vols. I and II,” Polygonal Pub-lishing House, Washington, 1983.
[3] S. Owa, “The Quasi-Hadamard Products of Certain Analytic Functions,” In: H. M. Srivastava and S. Owa, Eds., Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, 1992, pp. 234- 251.
[4] Z.-G. Wang, R. Aghalary, M. Darus and R. W. Ibrahim, “Some Properties of Certain Multivalent Analytic Functions Involving the Cho-Kwon-Srivastava Operator,” Journal of Mathematical and Computer Modelling, Vol. 49, No. 9-10, 2009, pp. 1969-1984.
[5] N. E. Cho, O. S. Kwon and H. M. Srivastava, “Inclusion Relationships and Argument Properties for Certain Subclasses of Multivalent Functions Associated with a Family of Linear Operators,” Journal of Mathematical Analysis and Applications, Vol. 292, No. 2, 2004, pp. 470-483. doi:10.1016/j.jmaa.2003.12.026
[6] R. Yamakawa, “Certain Subclasses of p-Valently Starlike Functions with Negative Coefficients,” In: H. M. Srivas- tava and S. Owa, Eds., Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, 1992, pp. 393-402.
[7] S. D. Bernardi, “Convex and Starlike Univalent Functions,” Transactions of the American Mathematical Society, Vol. 135, 1969, pp. 429-446. doi:10.1090/S0002-9947-1969-0232920-2
[8] A. E. Li-vingston, “On the Radius of Univalence of Certain Ana-lytic Functions,” Proceedings of the American Mathe-matical Society, Vol. 17, No. 2, 1966, pp. 352-357. doi:10.1090/S0002-9939-1966-0188423-X
[9] H. M. Srivastava and S. Owa (Eds.), “Current Topics in Analytic Function Theory,” World Scientific Publishing Company, Singapore, 1992.
[10] S. Owa, “On Distortion Theorems. I,” Kyungpook Mathematical Journal, Vol. 18, 1978, pp. 55-59.
[11] H. M. Srivastava and M. K. Aouf, “A Certain Fractional Derivative Operator and Its Applications to a New Class of Analytic and Multivalent Functions with Negative Coefficients. I and II,” Journal of Mathematical Analysis and Applications, Vol. 171, No. 1, 1992, pp. 1-13. doi:10.1006/jmaa.1995.1197
[12] A. Schild and H. Sil-verman, “Convolutions of Univalent Functions with Neg-ative Coefficients,” Annales Universitatis Mariae Cu-rie-Sklodowska Section A, Vol. 29, 1975, pp. 99-107.
[13] O. Altintas, H. Irmak and H. M. Srivastava, “Fractional Calculus and Certain Starlike Functions with Negative Coefficients,” Computers and Mathematics with Applications, Vol. 30, No. 2, 1995, pp. 9-15. doi:10.1016/0898-1221(95)00073-8
[14] M.-P. Chen, H. Irmak and H. M. Srivastava, “Some Families of Multiva-lently Analytic Functions with Negative Coefficients,” Journal of Mathematical Analysis and Applications, Vol. 214, No. 2, 1997, pp. 674-690. doi:10.1006/jmaa.1997.5615
[15] H. M. Srivastava and S. Owa (Eds.), “Univalent Functions, Fractional Calculus, and Their Applications,” Ellis Horwood Limited, Chiche-ster, 1989.

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