International Journal of Mathematics and Mathematical Sciences

Volume 2012 (2012), Article ID 362312, 21 pages

http://dx.doi.org/10.1155/2012/362312

Research Article

## Properties of Certain Subclass of Multivalent Functions with Negative Coefficients

^{1}Department of Mathematics, Chifeng University, Inner Mongolia, Chifeng 024000, China^{2}School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, China

Received 26 December 2011; Revised 26 March 2012; Accepted 27 March 2012

Academic Editor: Marianna Shubov

Copyright © 2012 Jingyu Yang and Shuhai Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- M. K. Aouf, H. M. Hossen, and H. M. Srivastava, “Some families of multivalent functions,”
*Computers & Mathematics with Applications*, vol. 39, no. 7-8, pp. 39–48, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - S. Owa, “Some properties of certain multivalent functions,”
*Applied Mathematics Letters*, vol. 4, no. 5, pp. 79–83, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - H. Saitoh, “A linear operator and its applications of first order differential subordinations,”
*Mathematica Japonica*, vol. 44, no. 1, pp. 31–38, 1996. View at Google Scholar · View at Zentralblatt MATH - H. M. Srivastava and J. Patel, “Some subclasses of multivalent functions involving a certain linear operator,”
*Journal of Mathematical Analysis and Applications*, vol. 310, no. 1, pp. 209–228, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - V. Kumar and S. L. Shukla, “Multivalent functions defined by Ruscheweyh derivatives. I, II,”
*Indian Journal of Pure and Applied Mathematics*, vol. 15, no. 11, pp. 1216–1238, 1984. View at Google Scholar - M. K. Aouf, H. Silverman, and H. M. Srivastava, “Some families of linear operators associated with certain subclasses of multivalent functions,”
*Computers & Mathematics with Applications*, vol. 55, no. 3, pp. 535–549, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - J. Sokół, “Classes of multivalent functions associated with a convolution operator,”
*Computers & Mathematics with Applications*, vol. 60, no. 5, pp. 1343–1350, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. K. Auof and H. E. Darwish, “Some classes of multivalent functions with negative coefficients. I,”
*Honam Mathematical Journal*, vol. 16, no. 1, pp. 119–135, 1994. View at Google Scholar · View at Zentralblatt MATH - S. L. Shukla and Dashrath, “On certain classes of multivalent functions with negative coefficients,”
*Soochow Journal of Mathematics*, vol. 8, pp. 179–188, 1982. View at Google Scholar · View at Zentralblatt MATH - S. K. Lee, S. Owa, and H. M. Srivastava, “Basic properties and characterizations of a certain class of analytic functions with negative coefficients,”
*Utilitas Mathematica*, vol. 36, pp. 121–128, 1989. View at Google Scholar - V. P. Gupta and P. K. Jain, “Certain classes of univalent functions with negative coefficients. II,”
*Bulletin of the Australian Mathematical Society*, vol. 15, no. 3, pp. 467–473, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - B. A. Uralegaddi and S. M. Sarangi, “Some classes of univalent functions with negative coefficients,”
*Analele Ştiinţifice ale Universităţii “Al. I. Cuza” din Iaşi*, vol. 34, no. 1, pp. 7–11, 1988. View at Google Scholar · View at Zentralblatt MATH - O. Altintas and S. Owa, “Neighborhoods of certain analytic functions with negative coefficients,”
*International Journal of Mathematics and Mathematical Sciences*, vol. 19, no. 4, pp. 797–800, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - O. Altintaş, Ö. Özkan, and H. M. Srivastava, “Neighborhoods of a class of analytic functions with negative coefficients,”
*Applied Mathematics Letters*, vol. 13, no. 3, pp. 63–67, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - O. Altintaş, Ö. Özkan, and H. M. Srivastava, “Neighborhoods of a certain family of multivalent functions with negative coefficients,”
*Computers & Mathematics with Applications*, vol. 47, no. 10-11, pp. 1667–1672, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. K. Aouf, “Neighborhoods of certain classes of analytic functions with negative coefficients,”
*International Journal of Mathematics and Mathematical Sciences*, vol. 2006, Article ID 38258, 6 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH *Univalent Functions, Fractional Calculus, and Their Applications*, Ellis Horwood Series: Mathematics, and Its Applications, Horwood, Chichester, UK.- M.-P. Chen, H. Irmak, and H. M. Srivastava, “Some families of multivalently analytic functions with negative coefficients,”
*Journal of Mathematical Analysis and Applications*, vol. 214, no. 2, pp. 674–690, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. II,”
*Journal of Mathematical Analysis and Applications*, vol. 192, no. 3, pp. 673–688, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - R. J. Libera, “Some classes of regular univalent functions,”
*Proceedings of the American Mathematical Society*, vol. 16, pp. 755–758, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - A. E. Livingston, “On the radius of univalence of certain analytic functions,”
*Proceedings of the American Mathematical Society*, vol. 17, pp. 352–357, 1966. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - H. M. Srivastava and S. Owa, Eds.,
*Current Topics in Analytic Function Theory*, World Scientific Publishing, River Edge, NJ, USA, 1992. - S. Owa, “On distortion theorem, I,”
*Kyungpook Mathematical Journal*, vol. 18, pp. 55–59, 1978. View at Google Scholar