User:Ardeshirshojaei/Aleksandrov–Rassias problem

The theory of isometries in the framework of Banach spaces has its beginning in a paper by Mazur and Ulam in 1932. They proved that every isometry of a normed real linear space onto a normed real linear space is a linear mapping up to translation. Aleksandrov asked whether the existence of a single conservative distance for some mapping implies that it is an isometry. Th.M. Rassias posed the following problem: ``If X and Y be normed linear spaces, and T be a continuous and/or surjective mapping satisfying the distance one preserving property (DOPP), then is T necessarily an isometry?'' This problem is called the Aleksandrov–Rassias problem.