Title : ( Differentiable Of Distance Functions In P-normed Spaces )
Authors: Mohammad Sal Moslehian , Asadollah Niknam , - - ,
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Abstract
The farthest point mapping in a p-normed space X is studied in virtue of the Gateaux derivative and the Frechet derivative. Let M be a closed bounded subset of X having the uniformly p-Gateaux differentiable norm. Under certain conditions, it is shown that every maximizing sequence is convergent, moreover, if M is a uniquely remotal set then the farthest point mapping is continuous and so M is singleton. In addition, a Hahn–Banach type theorem in p-normed spaces is proved.
Keywords
, Frechet derivative, quasi-norm, p-normed space, farthest mapping, Hahn-Banach theorem, remotal set.
@article{paperid:1012769,
author = {Sal Moslehian, Mohammad and Niknam, Asadollah and -, -},
title = {Differentiable Of Distance Functions In P-normed Spaces},
journal = {Australian Journal of Mathematical Analysis and Applications},
year = {2009},
volume = {6},
number = {1},
month = {October},
issn = {1449-5910},
pages = {1--10},
numpages = {9},
keywords = {Frechet derivative; quasi-norm; p-normed space; farthest mapping; Hahn-Banach theorem; remotal
set.},
}
%0 Journal Article
%T Differentiable Of Distance Functions In P-normed Spaces
%A Sal Moslehian, Mohammad
%A Niknam, Asadollah
%A -, -
%J Australian Journal of Mathematical Analysis and Applications
%@ 1449-5910
%D 2009
