A bounded subset $T$ of a metric space $(X,\rho)$ is said to be
remotal (uniquely remotal) if for each $x\in X$ there exists at
least one (exactly one) $t\in T$ such that
$\rho(x,t)=\sup\{\rho(x,y):y\in T\}.$ Such a point $t$ is called a
farthest point to $x$ in $T$. In this paper, we discuss properties
of remotal and uniquely remotal sets and, conditions under which
remotal and uniquely remotal sets are singleton. The underlying
spaces are convex metric spaces or externally convex metric spaces.
Publié le : 2011-03-15
Classification:
Farthest point,
farthest point map,
remotal set,
uniquely remotal set,
convex metric space,
$M$-space,
externally convex metric space and Chebyshev centre,
46B20,
46B99,
46C99,
46C15,
41A65
@article{1299766492,
author = {Narang, T. D. and Sangeeta,},
title = {On Singletonness of Remotal and Uniquely Remotal Sets},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {18},
number = {1},
year = {2011},
pages = { 113-120},
language = {en},
url = {http://dml.mathdoc.fr/item/1299766492}
}
Narang, T. D.; Sangeeta,. On Singletonness of Remotal and Uniquely Remotal Sets. Bull. Belg. Math. Soc. Simon Stevin, Tome 18 (2011) no. 1, pp. 113-120. http://gdmltest.u-ga.fr/item/1299766492/