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Abstract and Applied Analysis
Volume 2012, Article ID 638234, 13 pages
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.


We introduce an integrodifferential operator () which plays an important role in the Geometric Function Theory. Some theorems in differential subordination for () are used. Applications in Analytic Number Theory are also obtained which give new results for Hurwitz-Lerch Zeta function and Polylogarithmic function.