T. D. NARANG, SHAVETAMBRY TEJPAL and SANGEETA

On radial continuity of farthest point map

Pages 69-79
Received: 3 April 2006    Revised: 24 July 2006
Mathematics Subject Classification (2000): 41A65 - 54C60

Abstract Some new continuity concepts, called Outer Radially Lower (ORL), Outer Radially Upper (ORU) and Inner Radially Lower (IRL) for metric projection (nearest point map) and Inner Radially Upper (IRU) for anti metric projection (farthest point map) are known in the theory of nearest and farthest points in normed linear spaces (see e.g. B.Brosowski and F.Deutsch [Bull. Amer. Math. Soc. 78(1972), 974-978], B.B.Panda and O.P.Kapoor [J. Math. Anal. Appl. 62 (1978), 345-353]). In this paper we discuss all these concepts for the farthest point map when the underlying spaces are convex metric spaces.