- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Generalized isometry in normed spaces Commun. Korean Math. Soc.Published online June 10, 2021 Abbas Zivari-Kazempour Department of Mathematics, University of Ayatollah Borujerdi, Borujerd, Iran 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 : 46H40; 47A10 Full-Text :