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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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