On the Aleksandrov–rassias Problem of Distance Preserving Mappings

Abstract

In this paper, we introduce the concept of a semi-parallelogram and obtain some results for the Aleksandrov-Rassias problem using this concept. In particular, we resolve an important case of this problem for mappings preserving two distances with a nonintegral ratio.2010 Mathematics subject classification: primary 46B04; secondary 46B20, 46C05.