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2013 New Generalization of f -Best Simultaneous Approximation in Topological Vector Spaces
Mahmoud Rawashdeh, Sarah Khalil
Abstr. Appl. Anal. 2013: 1-7 (2013). DOI: 10.1155/2013/978738

Abstract

Let K be a nonempty subset of a Hausdorff topological vector space X , and let f be a real-valued continuous function on X . If for each x = ( x 1 , x 2 , , x n ) X n , there exists k 0 K such that F K ( x ) = i = 1 n f x i - k 0 = inf i = 1 n f ( x i - k ) : k K , then K is called f -simultaneously proximal and k 0 is called f -best simultaneous approximation for x in K . In this paper, we study the problem of f -simultaneous approximation for a vector subspace K in X . Some other results regarding f -simultaneous approximation in quotient space are presented.

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Mahmoud Rawashdeh. Sarah Khalil. "New Generalization of f -Best Simultaneous Approximation in Topological Vector Spaces." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/978738

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1279.41040
MathSciNet: MR3055968
Digital Object Identifier: 10.1155/2013/978738

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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