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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 904272, 13 pages
http://dx.doi.org/10.1155/2012/904272
Research Article

Sandwich-Type Theorems for a Class of Multiplier Transformations Associated with the Noor Integral Operators

1Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of korea
2Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan

Received 23 September 2011; Accepted 4 November 2011

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Nak Eun Cho and Khalida Inayat Noor. 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

  1. S. S. Miller and P. T. Mocanu, Differential Subordinations, Theory and Application, vol. 225 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker Inc., New York, NY, USA, 2000.
  2. S. S. Miller and P. T. Mocanu, “Subordinants of differential superordinations,” Complex Variables. Theory and Application, vol. 48, no. 10, pp. 815–826, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Y. Komatu, Distortion Theorems in Relation to Linear Integral Operators, vol. 385 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  4. T. M. Flett, “The dual of an inequality of Hardy and Littlewood and some related inequalities,” Journal of Mathematical Analysis and Applications, vol. 38, pp. 746–765, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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 Zentralblatt MATH · View at MathSciNet
  6. J.-L. Liu, “A linear operator and strongly starlike functions,” Journal of the Mathematical Society of Japan, vol. 54, no. 4, pp. 975–981, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. K. I. Noor, “On new classes of integral operators,” Journal of Natural Geometry, vol. 16, no. 1-2, pp. 71–80, 1999. View at Zentralblatt MATH
  8. 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 Zentralblatt MATH · View at MathSciNet
  9. J.-L. Liu, “The Noor integral and strongly starlike functions,” Journal of Mathematical Analysis and Applications, vol. 261, no. 2, pp. 441–447, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-L. Liu and K. I. Noor, “Some properties of Noor integral operator,” Journal of Natural Geometry, vol. 21, no. 1-2, pp. 81–90, 2002. View at Zentralblatt MATH
  11. K. I. Noor and M. A. Noor, “On integral operators,” Journal of Mathematical Analysis and Applications, vol. 238, no. 2, pp. 341–352, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. S. Miller, P. T. Mocanu, and M. O. Reade, “Subordination-preserving integral operators,” Transactions of the American Mathematical Society, vol. 283, no. 2, pp. 605–615, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. T. Bulboacă, “Integral operators that preserve the subordination,” Bulletin of the Korean Mathematical Society, vol. 34, no. 4, pp. 627–636, 1997. View at Zentralblatt MATH
  14. T. Bulboacă, “A class of superordination-preserving integral operators,” Indagationes Mathematicae. New Series, vol. 13, no. 3, pp. 301–311, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” The Michigan Mathematical Journal, vol. 28, no. 2, pp. 157–172, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. S. Miller and P. T. Mocanu, “Univalent solutions of Briot-Bouquet differential equations,” Journal of Differential Equations, vol. 56, no. 3, pp. 297–309, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, Germany, 1975.
  18. W. Kaplan, “Close-to-convex schlicht functions,” The Michigan Mathematical Journal, vol. 1, pp. 169–185, 1952. View at Zentralblatt MATH