Advances in Decision Sciences
Volume 2011 (2011), Article ID 167672, 9 pages
http://dx.doi.org/10.1155/2011/167672
Research Article

Majorization for A Subclass of 𝛽 -Spiral Functions of Order 𝛼 Involving a Generalized Linear Operator

Afaf A. Ali Abubaker,1 Maslina Darus,1 and Daniel Breaz2

1School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Malaysia
2Department of Mathematics-Informatics, Faculty of Sciences, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania

Received 22 June 2011; Accepted 18 August 2011

Academic Editor: Shelton Peiris

Copyright © 2011 Afaf A. Ali Abubaker et al. 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

Motivated by Carlson-Shaffer linear operator, we define here a new generalized linear operator. Using this operator, we define a class of analytic functions in the unit disk 𝑈 . For this class, a majorization problem of analytic functions is discussed.