Commun. Korean Math. Soc. 2022; 37(1): 105-112
Online first article June 10, 2021 Printed January 31, 2022
https://doi.org/10.4134/CKMS.c200451
Copyright © The Korean Mathematical Society.
Abbas Zivari-Kazempour
Ayatollah Borujerdi University
Let $g:Xlongrightarrow Y$ and $f:Ylongrightarrow Z$ be two maps between real normed linear spaces. Then $f$ is called generalized isometry or $g$-isometry if for each $x,y in X$, $$ Vert f(g(x))-f(g(y))Vert=Vert g(x)-g(y)Vert. $$ In this paper, under special hypotheses, we prove that each generalized isometry is affine. Some examples of generalized isometry are given as well.
Keywords: Isometry, Mazur-Ulam theorem, strictly convex, affine map
MSC numbers: Primary 46H40, 47A10
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