Open AccessOn Simultaneous Farthest Points in
Author(s) -
Sh. Al-Sharif,
Mahmoud S. Rawashdeh
Publication year - 2011
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/2011/890598
Subject(s) - mathematics , separable space , set (abstract data type) , banach space , bounded function , integrable system , space (punctuation) , set function , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , computer science , programming language , operating system
Let be a Banach space and let be a closed bounded subset of . For (1,2,…,)∈, we set (1,2,…,,)=sup{max1≤≤‖−‖∶∈}. The set is called simultaneously remotal if, for any (1,2,…,)∈, there exists ∈ such that (1,2,…,,)=max1≤≤‖−‖. In this paper, we show that if is separable simultaneously remotal in , then the set of ∞-Bochner integrable functions, ∞(,), is simultaneously remotal in ∞(,). Some other results are presented
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