摘要： n-isometries in quasi-β-n-normed spaces are studied and it's shown that every surjective mapping preserving n-distance one is an affine n-isometry in such spaces. The main tools in this manuscript are the fundamental theorems of affine geometry. Moreover, some statements which are equivalent to
characterizing mappings to be affine n-isometries in quasi-β-n-normed spaces are presented .