REMARKS ON REMOTAL SETS IN VETOR VALUED FUNCTION SPACES


Authors

M. SABABHEH - Department of Science and Humanities, Princess Sumaya University For Technology, Al Jubaiha, Amman 11941, Jordan.. R. KHALIL - Department of Mathematics, Jordan University, Al Jubaiha, Amman 11942, Jordan..


Abstract

Let \(X\) be a Banach space and \(E\) be a closed bounded subset of \(X\). For \(x \in X\) we set \(D(x,E) = \sup\{\| x − e \|: e \in E\}\). The set \(E\) is called remotal in \(X\) if for any \(x \in X\), there exists \(e \in E\) such that \(D(x,E) = \| x − e \|\) . It is the object of this paper to give new results on remotal sets in \(L^p(I,X)\), and to simplify the proofs of some results in [5].


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