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On Simultaneous Farthest Points in L∞(I,X) (2011)

Sh. Al-Sharif and M. Rawashdeh

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publication Date: 2011-07-22

Description: Let X be a Banach space and let G be a closed bounded subset of X. For (x1,x2,…,xm)∈Xm, we set ρ(x1,x2,…,xm,G)=sup⁡{max⁡1≤i≤m⁡‖xi−y‖:y∈G}. The set G is called simultaneously remotal if, for any (x1,x2,…,xm)∈Xm, there exists g∈G such that ρ(x1,x2,…,xm,G)=max⁡1≤i≤m⁡‖xi−g‖. In this paper, we show that if G is separable simultaneously remotal in X, then the set of ∞-Bochner integrable functions, L∞(I,G), is simultaneously remotal in L∞(I,X). Some other results are presented.

Print ISSN: 0161-1712

Electronic ISSN: 1687-0425

Topics: Mathematics

Published by Hindawi

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