On Simultaneous Approximation in Function Spaces

Abstract

The problem of simultaneous approximation in function spaces has attracted many researchers recently. Major results on the space of vector-valued continuous functions started to appear early nineties. In 2002, results on simultaneous approximation in p-Bochner integrable function spaces were published. The objective of this paper is to give a characterization for some subspaces of Bochner integrable functions space to be simultaneously proximinal.