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Journal of Function Spaces
Volume 2017, Article ID 7347130, 4 pages
Research Article

Best -Simultaneous Approximation in

Department of Mathematics, Faculty of Sciences, University of Alicante, 03080 Alicante, Spain

Correspondence should be addressed to Tijani Pakhrou;

Received 6 April 2017; Accepted 21 May 2017; Published 12 July 2017

Academic Editor: Yoshihiro Sawano

Copyright © 2017 Tijani Pakhrou. 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.


Let be a Banach space. Let and denote by the Banach space of all -valued Bochner -integrable functions on a certain positive complete -finite measure space , endowed with the usual -norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset of , the set is -simultaneously proximinal in for any arbitrary monotonous norm in .