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 Generalized isometry in normed spaces Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 105-112 https://doi.org/10.4134/CKMS.c200451Published online June 10, 2021Printed 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. Keywords : Isometry, Mazur-Ulam theorem, strictly convex, affine map MSC numbers : Primary 46H40, 47A10 Downloads: Full-text PDF   Full-text HTML

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