| The question of metric projection in Banach spaces is a continuous research topic, it has very important value in optimization, computational mathematics, equation theory and control theory. Continuity of metric projection is studied forever. Up to now, continuity of metric projection haven't been very perfect in a dual spaces of Banach spaces X . In this paper, I mainly explore the representation of the metric projections of hyperplances, aw approximation set, and the relation between ( S-K)property and continuity of metric projection. In the process of my study, I have obtained some productive results.This paper consists of three parts.Charpter one In this chapter , we give a representation of the metric pr -ojections on a class of hyperplances in the dual spaces of Banach spaces. For some special Banach Spaces, some results of continuity of the metric projecti -ons on a class of hyperplane in X or X~*are obtained.Charpter two In this chapter, we mainly study the relations between weakly approximation set and aw approximation compact set(approximation set and aw approximation compact set ) in weakly locally uniform convex spaces (compact locally uniform convex space). we prove that if X is weakly locally uniform convex spaces (compact locally uniform convex space) and G -X is aw approximation convex set ( aw approximation set), then PG is norm-weakly (norm-norm) upper semi-continuity.Charpter three In this chapter, we study the problems about continuity of the metric projections in dual spaces of X which have the property (S-K), and obtained some results about continuity of the metric projections. |
