[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c200451

GENERALIZED ISOMETRY IN NORMED SPACES

Zivari-Kazempour, Abbas (Department of Mathematics Ayatollah Borujerdi University)

Publication Information

Communications of the Korean Mathematical Society / v.37, no.1, 2022 , pp. 105-112 More about this Journal

Abstract

Let g : X ⟶ Y and f : Y ⟶ Z be two maps between real normed linear spaces. Then f is called generalized isometry or g-isometry if for each x, y ∈ X, ║f(g(x)) - f(g(y))║ = ║g(x) - g(y)║. 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;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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