Abstract and Applied Analysis
Volume 2013 (2013), Article ID 978738, 7 pages
http://dx.doi.org/10.1155/2013/978738
Research Article

New Generalization of -Best Simultaneous Approximation in Topological Vector Spaces

Mahmoud Rawashdeh and Sarah Khalil

Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan

Received 20 January 2013; Revised 23 April 2013; Accepted 23 April 2013

Academic Editor: Naseer Shahzad

Copyright © 2013 Mahmoud Rawashdeh and Sarah Khalil. 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

Let be a nonempty subset of a Hausdorff topological vector space , and let be a real-valued continuous function on . If for each , there exists such that , then is called -simultaneously proximal and is called -best simultaneous approximation for in . In this paper, we study the problem of -simultaneous approximation for a vector subspace in . Some other results regarding -simultaneous approximation in quotient space are presented.