Convergence Theorems for Best Approximations in a Nonreflexive Banach Space Original Research Article

In this paper, we study continuity properties of the mappingP: (x, A)→PA(x) in a nonreflexive Banach space where PA is the metric projection onto A. Our results extend the existing convergence theorems on the best approximations in a reflexive Banach space to nonreflexive Banach spaces by using Wijsman convergence of sets.