WELL-POSEDNESS OF GENERALIZED BEST APPROXIMATION PROBLEMS

Abstract

Given a closed subset A of a Banach space X, a point x in X and a continuous function f : X-->R^1, we consider the problem of finding a solution to the minimization problem min{f (x-y): y in A}. For a fixed function f, we define an appropriate complete metric space M of all pairs (A, x) and construct a subset ­ of Mwhich is a countable intersection of open everywhere dense sets such that for each pair in ­ our minimization problem is well posed.