ISRN Mathematical Analysis

Volume 2012 (2012), Article ID 632429, 9 pages

http://dx.doi.org/10.5402/2012/632429

Research Article

## Subclasses of Analytic Functions Associated with Generalised Multiplier Transformations

^{1}Faculty of Computer and Mathematical Sciences, MARA University of Technology, 40450 Shah Alam, Selangor, Malaysia^{2}Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 20 January 2012; Accepted 25 March 2012

Academic Editors: O. Miyagaki and W. Yu

Copyright © 2012 Rashidah Omar and Suzeini Abdul Halim. 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

- A. Cǎtaş, “On certain classes of p-valent functions defined by new multiplier transformations,”
*TC Istanbul Kultur University Publications, TC Istanbul kultur University*, vol. 91, pp. 241–250, 2008, Proceedings of the International Symposium on Geometric Function Theory and Applications (GFTA '07), Istanbul, Turkey, August 2007. View at Google Scholar - A. Cǎtaş, G. I. Oros, and G. Oros, “Differential subordinations associated with multiplier transformations,”
*Abstract and Applied Analysis*, vol. 2008, Article ID 845724, 11 pages, 2008. View at Google Scholar - A. Cǎtaş, “Neighborhoods of a certain class of analytic functions with negative coefficients,”
*Banach Journal of Mathematical Analysis*, vol. 3, no. 1, pp. 111–121, 2009. View at Google Scholar · View at Scopus - N. E. Cho and K. I. Noor, “Sandwich-type theorems for a class of multiplier transformations associated with the Noor integral operators,”
*Abstract and Applied Analysis*, vol. 2012, Article ID 904272, 13 pages, 2012. View at Google Scholar - R. M. El-Ashwah, M. K. Aouf, and S. M. El-Deeb, “On a class of multivalent functions defined by an extended multiplier transformations,”
*Computers and Mathematics with Applications*, vol. 60, no. 3, pp. 623–628, 2010. View at Publisher · View at Google Scholar · View at Scopus - A. A. Lupaş, “A note on a subclass of analytic functions defined by Ruscheweyh derivative and multiplier transformations,”
*International Journal of Open Problems in Complex Analysis*, vol. 2, no. 2, pp. 60–66, 2010. View at Google Scholar - K. I. Noor, “On new classes of integral operators,”
*Journal of Natural Geometry*, vol. 16, pp. 71–80, 1999. View at Google Scholar - S. R. Mondal and A. Swaminathan, “Geometric properties of generalized polylogarithm,”
*Integral Transforms and Special Functions*, vol. 21, no. 9, pp. 691–701, 2010. View at Publisher · View at Google Scholar · View at Scopus - N. E. Cho and J. A. Kim, “Inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation,”
*Computers and Mathematics with Applications*, vol. 52, no. 3-4, pp. 323–330, 2006. View at Publisher · View at Google Scholar · View at Scopus - J. H. Choi, M. Saigo, and H. M. Srivastava, “Some inclusion properties of a certain family of integral operators,”
*Journal of Mathematical Analysis and Applications*, vol. 276, no. 1, pp. 432–445, 2002. View at Publisher · View at Google Scholar · View at Scopus - O. S. Kwon and N. E. Cho, “Inclusion properties for certain subclasses of analytic functions associated with the Dziok-Srivastava operator,”
*Journal of Inequalities and Applications*, vol. 2007, Article ID 51079, 10 pages, 2007. View at Google Scholar - N. E. Cho and H. M. Srivastava, “Argument estimates of certain analytic functions defined by a class of multiplier transformations,”
*Mathematical and Computer Modelling*, vol. 37, no. 1-2, pp. 39–49, 2003. View at Google Scholar · View at Scopus - F. M. Al-Oboudi, “On univalent functions defined by derivative operator,”
*International Journal of Mathematics and Mathematical Sciences*, vol. 27, pp. 1429–1436, 2004. View at Google Scholar - G. S. Salagean, “Subclasses of univalent functions,” in
*Proceedings of the Complex Analysis 5th Romanian-Finnish Seminar, Part 1*, vol. 1013, pp. 362–372, Springer, 1983. - B. A. Uralegaddi and C. Somanatha, “Certain classes of univalent functions,” in
*Current Topics in Analytic Function Theory*, pp. 371–374, World Scientific, River Edge, NJ, USA, 1992. View at Google Scholar - W. Ma and D. Minda, “A unified treatment of some special classes of univalent functions,” in
*Proceedings of the Conference on Complex Analysis*, Z. Li, F. Ren, L. Yang, and S. Zhang, Eds., pp. 157–169, International Press, Cambridge, Mass, USA, 1992. - W. Janowski, “Some extremal problems for certain families of analytic functions I,”
*Annales Polonici Mathematici*, vol. 28, pp. 297–326, 1973. View at Google Scholar - R. Omar and S. A. Halim, “Classes of functions defined by Dziok-Srivastavaoperator,”
*Far East Journal of Mathematical Sciences*. In press. - P. Enigenberg, S. S. Miller, P. T. Mocanu, and M. O. Reade, “On a Briot-Bouquet differential subordination,”
*General Inequalities*, vol. 3, pp. 339–348, 1983. View at Google Scholar - S. S. Miller and P. T. Mocanu, “Differential subordination and univalent functions,”
*The Michigan Mathematical Journal*, vol. 28, pp. 157–171, 1981. View at Google Scholar - S. D. Bernardi, “Convex and starlike univalent functions,”
*Transactions of the American Mathematical Society*, vol. 135, pp. 429–446, 1969. View at Google Scholar - I. B. Jung, Y. C. Kim, and H. M. Srivastava, “The Hardy space of analytic functions associated with certain one-parameter families of integral operators,”
*Journal of Mathematical Analysis and Applications*, vol. 176, no. 1, pp. 138–147, 1993. View at Publisher · View at Google Scholar · View at Scopus - R. J. Libera, “Some classes of regular univalent functions,”
*Proceedings of the American Mathematical Society*, vol. 16, pp. 755–758, 1965. View at Google Scholar - A. E. Livington, “On the radius of univalence of certain analytic functions,”
*Proceedings of the American Mathematical Society*, vol. 17, pp. 352–357, 1966. View at Google Scholar