Generalized isometry in normed spaces
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초록
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.
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.
참고문헌 (10)
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