On Certain Subclasses of Multivalent Functions Associated with a Family of Linear Operators
Jae Ho Choi
.
DOI: 10.4236/apm.2011.14040   PDF   HTML     4,430 Downloads   9,004 Views   Citations

Abstract

Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.

Share and Cite:

J. Choi, "On Certain Subclasses of Multivalent Functions Associated with a Family of Linear Operators," Advances in Pure Mathematics, Vol. 1 No. 4, 2011, pp. 228-234. doi: 10.4236/apm.2011.14040.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] 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
[2] B. C. Carlson and D. B. Shaffer, “Starlike and Prestarlike Hypergeometric Functions,” SIAM Journal on Mathematical Analysis, Vol. 15, No. 4, 1984, pp. 737-745. doi:10.1137/0515057
[3] N. K. 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 Operator,” Journal of Mathematical Analysis and Applications, Vol. 292, No. 2, 2004, pp. 470-483. doi:10.1016/j.jmaa.2003.12.026
[4] A. W. Goodman, “Uni-valent Functions, Vol. I, II,” Polygonal Publishing House, Washington, 1983.
[5] J.-L. Liu and K. I. Noor, “Some Properties of Noor Integral Operator,” Journal of Natural Ge-ometry, Vol. 21, 2002, pp. 81-90.
[6] S. S. Miller, “Differen-tial Inequalities and Caratheodory Functions,” Bulletin of the American Mathematical Society, Vol. 81, 1975, pp. 78-81. doi:10.1090/S0002-9904-1975-13643-3
[7] K. I. Noor, “On Subclasses of Close-to-Convex Functions of Higher Order,” International Journal of Mathematics and Mathematical Sci-ences, Vol. 15, No. 2, 1992, pp. 279-289. doi:10.1155/S016117129200036X
[8] K. I. Noor, “On New Classes of Integral Operators,” Journal of Natural Geometry, Vol. 16, 1999, pp. 71-80.
[9] K. I. Noor and M. Arif, “Gen-eralized Integral Operators Related with p-Valent Analytic Functions,” Mathematical Inequalities Applications, Vol. 12, No. 1, 2009, pp. 91-98.
[10] J. Patal and N. E. Cho, “Some Classes of Analytic Functions Involving Noor Integral Opera-tor,” Journal of Mathematical Analysis and Applications, Vol. 312, No. 2, 2005, pp. 564-575. doi:10.1016/j.jmaa.2005.03.047
[11] B. Pinchuk, “Functions with Bounded Boundary Rotation,” Israel Journal of Mathe-matics, Vol. 10, No. 1, 1971, pp. 7-16. doi:10.1007/BF02771515
[12] S. Ponnusamy, “Differential Subordination and Bazilevic Functions,” Proceedings Mathe-matical Sciences, Vol. 105, No. 2, 1995, pp. 169-186. doi:10.1007/BF02880363
[13] H. Saitoh, “A Linear Operator and Its Applications of First Order Differential Subordina-tions,” Mathematica Japonica, Vol. 44, 1996, pp. 31-38.
[14] J. Sokó? and L. Trojnar-Spelina, “Convolution Properties for Certain Classes of Multivalent Functions,” Journal of Mathematical Analysis and Applications, Vol. 337, No. 2, 2008, pp. 1190-1197. doi:10.1016/j.jmaa.2007.04.055
[15] H. M. Srivastava and S. Owa (Eds.), “Current Topics in analytic Function Theory,” World Scientific, Singapore, 1992.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.