A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces

	A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces
Iranian Journal of Fuzzy Systems
مقاله 9، دوره 7، شماره 2، شهریور 2010، صفحه 109-119 اصل مقاله (208.49 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2010.179
نویسنده
Cihangir Alaca^*
Department of Mathematics, Faculty of Science and Arts, Sinop University, 57000 Sinop, Turkey
چکیده
In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$% -Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give a new 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, that is, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$% -fuzzy $2$-normed linear space is affine.
کلیدواژه‌ها
$alpha $-$2$-Norm؛ $2$-Fuzzy $2$-Normed linear spaces؛ $2$-Isometry؛ $2$-Lipschitz mapping

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