This paper studies the generalized 2-isometry and gives a different version of Mazur-Ulam theorem. We show that every generalized area n preserving mapping between real 2-normed linear spaces X and Y which is strictly convex is affine under some conditions.
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.
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