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Turkish Journal of Mathematics

Authors

EYAD ABU-SIRHAN

DOI

10.3906/mat-0904-37

Abstract

Let Z be a Banach space and G be a closed subspace of Z. For f_1,f_2 \in Z, the distance from f_1,f_2 to G is defined by d(f_1,f_2,G) = \underset{f \in G}{\inf} max { f_1-f , f_2-f }. An element g^{\ast} \in G satisfying max { f_1-g^{\ast } , f_2-g^{\ast } } = \underset{f \in G}{\inf } max { f_1-f , f_2-f } is called a best simultaneous approximation for f_1,f_2 from G. In this paper, we study the problem of best simultananeous approximation in the space of all continuous X-valued functions on a compact Hausdorff space S; C(S,X), and the space of all Bounded linear operators from a Banach space X into a Banach space Y; L(X,Y).

First Page

101

Last Page

112

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Mathematics Commons

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