Tokyo Journal of Mathematics, Volume (41), No (1), Year (2018-1) , Pages (253-272)

Title : ( Geometric aspects of $p$-angular and skew p-angular distances )

Authors: J. Rooin , S. Habibzadeh , Mohammad Sal Moslehian ,

Access to full-text not allowed by authors

Citation: BibTeX | EndNote


‎Corresponding to the concept of $p$-angular distance $\alpha_p[x,y]:=\left\lVert\lVert x\rVert^{p-1}x-\lVert y\rVert^{p-1}y\right\rVert$‎, ‎we first introduce the notion of skew $p$-angular distance $\beta_p[x,y]:=\left\lVert \lVert y\rVert^{p-1}x-\lVert x\rVert^{p-1}y\right\rVert$ for non-zero elements of $x‎, ‎y$ in a real normed linear space and study some of significant geometric properties of the $p$-angular and the skew $p$-angular distances‎. ‎We then give some results comparing two different $p$-angular distances with each other‎. ‎Finally‎, ‎we present some characterizations of inner product spaces related to the $p$-angular and the skew $p$-angular distances‎. ‎In particular‎, ‎we show that if $p>1$ is a real number‎, ‎then a real normed space $\mathcal{X}$ is an inner product space‎, ‎if and only if for any $x,y\in \mathcal{X}\smallsetminus{\lbrace 0\rbrace}$‎, ‎it holds that $\alpha_p[x,y]\geq\beta_p[x,y]$‎.


, $p$-angular distance‎, ‎skew $p$-angular distance‎, ‎inequality‎, ‎characterization of inner product spaces.
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

author = {J. Rooin and S. Habibzadeh and Sal Moslehian, Mohammad},
title = {Geometric aspects of $p$-angular and skew p-angular distances},
journal = {Tokyo Journal of Mathematics},
year = {2018},
volume = {41},
number = {1},
month = {January},
issn = {0387-3870},
pages = {253--272},
numpages = {19},
keywords = {$p$-angular distance‎; ‎skew $p$-angular distance‎; ‎inequality‎; ‎characterization of inner product spaces.},


%0 Journal Article
%T Geometric aspects of $p$-angular and skew p-angular distances
%A J. Rooin
%A S. Habibzadeh
%A Sal Moslehian, Mohammad
%J Tokyo Journal of Mathematics
%@ 0387-3870
%D 2018