CONVERGENCE THEOREMS FOR BEST APPROXIMATIONS IN A NONREFLEXIVE BANACH-SPACE

In this paper, we study continuity properties of the mapping P: (x, A) --> P-A(x) in a nonreflexive Banach space where P-A is the metric pro jection onto A. Our results extend the existing convergence theorems o n the best approximations in a reflexive Banach space to nonreflexive Banach spaces by using Wijsman convergence of sets. (C) 1998 Academic Press.