Best simultaneous approximation in normed linear spaces

Abstract

In this thesis we consider the problem of simultaneously approximating elements of a set B C X by a single element of a set K C X. This type of a problem arises when the element to be approximated is not known precisely but is known to belong to a set.Thus, best simultaneous approximation is a natural generalization of best approximation which has been studied extensively. The theory of best simultaneous approximation has been studied by many authors, see for example [4], [8], [25], [28], [26] and [12] to name but a few.