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

Document Type: Research Paper


Department of Mathematics, Faculty of Science and Arts, Sinop University, 57000 Sinop, Turkey


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.