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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 150571, 10 pages
http://dx.doi.org/10.1155/2012/150571
Research Article

On Subclass of ๐‘˜ -Uniformly Convex Functions of Complex Order Involving Multiplier Transformations

Department of Mathematics, College of Computer Science and Mathematics, University of Al-Qadisiya, Diwaniya, Iraq

Received 30 December 2011; Revised 28 February 2012; Accepted 13 March 2012

Academic Editor: Ondřej Došlý

Copyright © 2012 Waggas Galib Atshan and Ali Hamza Abada. 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

We introduce a subclass of ๐‘˜ -uniformly convex functions of order ๐›ผ with negative coefficients by using the multiplier transformations in the open unit disk ๐‘ˆ = { ๐‘ง โˆˆ โ„‚ โˆถ | ๐‘ง | < 1 } . We obtain coefficient estimates, radii of convexity and close-to-convexity, extreme points, and integral means inequalities for the function ๐‘“ that belongs to the class ๐’ฉ โ„“ ๐‘š ( ๐›ผ , ๐›ฝ , ๐‘˜ , ๐œ ) .