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...

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...

The classical Mazur–Ulam theorem which states that every sur-jective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...

The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...

We prove a local version of the Mazur-Ulam theorem.

The aim of this article is to proved a Mazur-Ulam type theorem in the strictly convex fuzzy anti-normed spaces.