About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 274985, 17 pages
http://dx.doi.org/10.1155/2012/274985
Research Article

Generalized k-Uniformly Close-to-Convex Functions Associated with Conic Regions

Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

Received 24 January 2012; Accepted 31 January 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Khalida Inayat Noor. 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 define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close-to-convexity. Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed. The results are shown to be the best possible.