Let X be a normed space, G a nonempty bounded subset of X and fxng a bounded
sequence in X. In this article, we introduce and discuss the concept of
asymptotic farthest points of fxng in G, which is a new definition in
abstract approximation theory. Then, by applying the topics of functional
analysis, we investigate the relation between this new concept and the
concepts of extreme points and convexity. In particular, one of the main
purposes of this paper is to study conditions under which the existence
(uniqueness) of asymptotic farthest point of fxng in G is equivalent to the
existence (uniqueness) of asymptotic farthest point of fxng in ext(G) or
co(G).
Trends in functional analysis and approximation theory
