Weighted Mazur-Ulam spaces

摘要

The notion of a Mazur-Ulam space, introduced by C. P. Niculescu in [6] by using the midpoints, is extended here for an arbitrary weight lambda a (0, 1). A similar characterization in terms of a class of isometries and their unique fixed point is obtained for the rational case lambda = m and under more complicated conditions than that of in [6] or [7, p. 166].