Inequalities in Additive N-isometries on Linear N-normed Banach Spaces

Research Article Inequalities in Additive N-isometries on Linear N-normed Banach Spaces

Aleksandrov problem. Examine whether the existence of a single conservative distance for some mapping T implies that T is an isometry. The Aleksandrov problem has been investigated in several papers (see [2, 3, 6–9, 13– 15, 20, 23, 26, 28]). Rassias and Šemrl [25] proved the following theorem for mappings satisfying the strong distance one preserving property (SDOPP), that is, for every x, y ∈ ...

ISOMETRY ON LINEAR n-NORMED SPACES

This paper generalizes the Aleksandrov problem, the Mazur–Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an nisometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.

ON n-NORMED SPACES

Given ann-normed space withn≥ 2, we offer a simple way to derive an (n−1)norm from the n-norm and realize that any n-normed space is an (n−1)-normed space. We also show that, in certain cases, the (n−1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n− 1)-norm. Using this fact, we prove a fixed point t...

BEST APPROXIMATION SETS IN -n-NORMED SPACE CORRESPONDING TO INTUITIONISTIC FUZZY n-NORMED LINEAR SPACE

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.

Partial Isometries on Banach Spaces