Title : ( Characterization of a generalized triangle inequality in normed spaces )
Authors: farzad dadipour , Mohammad Sal Moslehian , John M. Rassias , Sin-Ei Takahasi ,
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Abstract
For a normed linear space (X, | cdot |) and p>0 we characterize all n -tuples ( mu_1, cdots, mu_n) in mathbb{R}^{n} for which the generalized triangle inequality of the second type |x_1+ cdots+x_n |^p leq frac{ |x_1 |^p}{ mu_1}+ cdots+ frac{ |x_n |^p}{ mu_n} holds for any x_1, cdots,x_n in X . We also characterize ( mu_1, cdots, mu_n) in mathbb{R}^{n} for which the reverse of the inequality above holds.
Keywords
generalized triangle inequality; norm inequality; triangle inequality of the second type; normed space.
@article{paperid:1023357,
author = {Dadipour, Farzad and Sal Moslehian, Mohammad and John M. Rassias and Sin-Ei Takahasi},
title = {Characterization of a generalized triangle inequality in normed spaces},
journal = {Nonlinear Analysis: Theory, Methods & Applications},
year = {2012},
volume = {75},
number = {2},
month = {January},
issn = {0362-546X},
pages = {735--741},
numpages = {6},
keywords = {generalized triangle inequality; norm inequality; triangle inequality of the second type; normed space.},
}
%0 Journal Article
%T Characterization of a generalized triangle inequality in normed spaces
%A Dadipour, Farzad
%A Sal Moslehian, Mohammad
%A John M. Rassias
%A Sin-Ei Takahasi
%J Nonlinear Analysis: Theory, Methods & Applications
%@ 0362-546X
%D 2012
