Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 105-112 https://doi.org/10.4134/CKMS.c200451 Published online June 10, 2021 Printed January 31, 2022
Abbas Zivari-Kazempour Ayatollah Borujerdi University
Abstract : Let $g:X\longrightarrow Y$ and $f:Y\longrightarrow Z$ 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.
