Global Version of Bjornestal's Estimate for Metric Projection Operator in Banach Space

TL;DR

This paper extends Bjornestal's local estimate of the metric projection operator's continuity to a global setting for arbitrary closed convex sets in Banach spaces, broadening the understanding of projection behavior.

Contribution

It provides the first global estimate for the metric projection operator on any closed convex set in Banach spaces, generalizing previous local results.

Findings

Established a global modulus of continuity for the metric projection operator.

Extended the applicability of projection estimates from subspaces to arbitrary convex sets.

Enhanced theoretical understanding of projection operators in Banach spaces.

Abstract

In 1979, B.Bjornestal obtained local estimate for a modulus of uniform continuity of metric projection operator on closed subspace in uniformly convex and uniformly smooth Banach space $B$. In the present paper we give the global version of this result for the projection operator on an arbitrary closed convex set in $B$.