About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 638234, 13 pages
http://dx.doi.org/10.1155/2012/638234
Research Article

Differential Subordination Results for Certain Integrodifferential Operator and Its Applications

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura 35516, Egypt
3Department of Mathematics, College of Science, University of Hail, Hail, Saudi Arabia

Received 8 October 2012; Accepted 27 November 2012

Academic Editor: Josip E. Pecaric

Copyright © 2012 M. A. Kutbi and A. A. Attiya. 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. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
  2. J. Choi, D. S. Jang, and H. M. Srivastava, “A generalization of the Hurwitz-Lerch zeta function,” Integral Transforms and Special Functions, vol. 19, no. 1-2, pp. 65–79, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. C. Ferreira and J. L. López, “Asymptotic expansions of the Hurwitz-Lerch zeta function,” Journal of Mathematical Analysis and Applications, vol. 298, no. 1, pp. 210–224, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. P. L. Gupta, R. C. Gupta, S.-H. Ong, and H. M. Srivastava, “A class of Hurwitz-Lerch zeta distributions and their applications in reliability,” Applied Mathematics and Computation, vol. 196, no. 2, pp. 521–531, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Q.-M. Luo and H. M. Srivastava, “Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials,” Journal of Mathematical Analysis and Applications, vol. 308, no. 1, pp. 290–302, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. M. A. Kutbi and A. A. Attiya, “Differential subordination result with the Srivastava-Attiya integral operator,” Journal of Inequalities and Applications, vol. 2010, Article ID 618523, 10 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. G. Murugusundaramoorthy, “Subordination results for spiral-like functions associated with the Srivastava-Attiya operator,” Integral Transforms and Special Functions, vol. 23, no. 2, pp. 97–103, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. M. Srivastava and A. A. Attiya, “An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination,” Integral Transforms and Special Functions, vol. 18, no. 3-4, pp. 207–216, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. Owa and A. A. Attiya, “An application of differential subordinations to the class of certain analytic functions,” Taiwanese Journal of Mathematics, vol. 13, no. 2A, pp. 369–375, 2009. View at Zentralblatt MATH
  10. N. E. Cho, I. H. Kim, and H. M. Srivastava, “Sandwich-type theorems for multivalent functions associated with the Srivastava-Attiya operator,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 918–928, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. E. A. Elrifai, H. E. Darwish, and A. R. Ahmed, “Some applications of Srivastava-Attiya operator to p-valent starlike functions,” Journal of Inequalities and Applications, vol. 2010, Article ID 790730, 11 pages, 2010. View at Publisher · View at Google Scholar
  12. J.-L. Liu, “Sufficient conditions for strongly star-like functions involving the generalized Srivastava-Attiya operator,” Integral Transforms and Special Functions, vol. 22, no. 2, pp. 79–90, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. M. H. Mohd and M. Darus, “Differential subordination and superordination for Srivastava-Attiya operator,” International Journal of Differential Equations, vol. 2011, Article ID 902830, 19 pages, 2011. View at Publisher · View at Google Scholar
  14. K. I. Noor and S. Z. H. Bukhari, “Some subclasses of analytic and spiral-like functions of complex order involving the Srivastava-Attiya integral operator,” Integral Transforms and Special Functions, vol. 21, no. 12, pp. 907–916, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. S.-M. Yuan and Z.-M. Liu, “Some properties of two subclasses of k-fold symmetric functions associated with Srivastava-Attiya operator,” Applied Mathematics and Computation, vol. 218, no. 3, pp. 1136–1141, 2011. View at Publisher · View at Google Scholar
  16. Z.-G. Wang, Z.-H. Liu, and Y. Sun, “Some properties of the generalized Srivastava-Attiya operator,” Integral Transforms and Special Functions, vol. 23, no. 3, pp. 223–236, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. W. Alexander, “Functions which map the interior of the unit circle upon simple regions,” Annals of Mathematics, vol. 17, no. 1, pp. 12–22, 1915. View at Publisher · View at Google Scholar
  18. 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
  19. S. D. Bernardi, “Convex and starlike univalent functions,” Transactions of the American Mathematical Society, vol. 135, pp. 429–446, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. 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
  21. J.-L. Liu, “Subordinations for certain multivalent analytic functions associated with the generalized Srivastava-Attiya operator,” Integral Transforms and Special Functions, vol. 19, no. 11-12, pp. 893–901, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. J. K. Prajapat and S. P. Goyal, “Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions,” Journal of Mathematical Inequalities, vol. 3, no. 1, pp. 129–137, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. G. Sălăgean, “Subclasses of univalent functions,” in Complex Analysis, vol. 1013 of Lecture Notes in Mathematics, pp. 362–372, Springer, Berlin, Germany, 1983, Proceedings of the 5h Romanian-Finnish Seminar, Part 1, Bucharest, Romania, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. F. M. Al-Oboudi, “On univalent functions defined by a generalized Salagean operator,” International Journal of Mathematics and Mathematical Sciences, no. 25–28, pp. 1429–1436, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. N. E. Cho and T. H. Kim, “Multiplier transformations and strongly close-to-convex functions,” Bulletin of the Korean Mathematical Society, vol. 40, no. 3, pp. 399–410, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. 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 Zentralblatt MATH
  28. D. J. Hallenbeck and S. Ruscheweyh, “Subordination by convex functions,” Proceedings of the American Mathematical Society, vol. 52, pp. 191–195, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. S. S. Miller and P. T. Mocanu, “Marx-Strohhäcker differential subordination systems,” Proceedings of the American Mathematical Society, vol. 99, no. 3, pp. 527–534, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, vol. 225 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000.