Asymptotic farthest points and extreme points

The Mazur Intersection Property and Farthest Points

K. S. Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.

On co-Farthest Points in Normed Linear Spaces

In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditions...

Concerning weak ∗ - extreme points

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.

Nearest and farthest points in spaces of curvature bounded below

Let A be a nonempty closed subset (resp. nonempty bounded closed subset) of a metric space (X, d) and x ∈ X \ A. The nearest point problem (resp. the farthest point problem) w.r.t. x considered here is to find a point a0 ∈ A such that d(x, a0) = inf{d(x, a) : a ∈ A} (resp. d(x, a0) = sup{d(x, a) : a ∈ A}). We study the well posedness of nearest point problems and farthest point problems in geod...

Farthest Neighbors and Center Points in the Presen