Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 401913, 16 pages
doi:10.1155/2011/401913
Research Article

On Certain Subclasses of Meromorphically 𝑝 -Valent Functions Associated by the Linear Operator 𝐷 𝑛 𝜆

Amin Saif and Adem Kılıçman

Department of Mathematics, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

Received 26 July 2010; Accepted 28 February 2011

Academic Editor: Jong Kim

Copyright © 2011 Amin Saif and Adem Kılıçman. 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.

Abstract

The purpose of this paper is to introduce two novel subclasses Γ 𝜆 ( 𝑛 , 𝛼 , 𝛽 ) and Γ ∗ 𝜆 ( 𝑛 , 𝛼 , 𝛽 ) of meromorphic 𝑝 - valent functions by using the linear operator 𝐷 𝑛 𝜆 . Then we prove the necessary and sufficient conditions for a function 𝑓 in order to be in the new classes. Further we study several important properties such as coefficients inequalities, inclusion properties, the growth and distortion theorems, the radii of meromorphically 𝑝 - valent starlikeness, convexity, and subordination properties. We also prove that the results are sharp for a certain subclass of functions.