A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces
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Abstract:
In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space is affine.
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Journal title
volume 7 issue 2
pages 109- 119
publication date 2010-06-06
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