<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Some new continuity concepts called Outer Radially Lower(ORL), Outer Radially Upper (ORU) and Inner Radially Lower (IRL), for set-valued metric projections were introduced in Banach spaces by B. Brosowski and F. Deutsch [Bull. Amer. Math. Soc. 78(1972), 974-978] to characterize suns and Chebyshev sets. In this paper we extend these concepts together with the concept of Inner Radially Upper (IRU) continuity to convex metric spaces and prove some results including those of Brosowski and Deutsch in such spaces.</p></abstract>

Some new continuity concepts called Outer Radially Lower(ORL), Outer Radially Upper (ORU) and Inner Radially Lower (IRL), for set-valued metric projections were introduced in Banach spaces by B. Brosowski and F. Deutsch [Bull. Amer. Math. Soc. 78(1972), 974-978] to characterize suns and Chebyshev sets. In this paper we extend these concepts together with the concept of Inner Radially Upper (IRU) continuity to convex metric spaces and prove some results including those of Brosowski and Deutsch in such spaces.

On Radial Continuity of Metric Projections

Department of Mathematics Guru Nanak Dev University

Annals of West University of Timisoara - Mathematics and Computer Science

{"article-title":"On Radial Continuity of Metric Projections"}

Some new continuity concepts called Outer Radially Lower(ORL), Outer Radially Upper (ORU) and Inner Radially Lower (IRL), for set-valued metric projections...

On Radial Continuity of Metric Projections

Published Online: Jan 15, 2013

Page range: 67 - 83

DOI: https://doi.org/10.2478/v10324-012-0016-1

This content is open access.