AN INEQUALITY FOR DISTANCES AMONG FIVE POINTS AND DISTANCE PRESERVING MAPPINGS

Abstract

Using properties of norm and inner product, we prove a new inequality for distances between five points arbitrarily given in an inner product space. Moreover, we investigate the Aleksandrov-Rassias problem by proving that if the distance 1 is contractive and the golden ratio is extensive by a mapping f, then f is a linear isometry up to translation.