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A fixed point approach to the stability of isometries. (English) Zbl 1153.39309
Summary: We apply a fixed point theorem to the proof of Hyers-Ulam-Rassias stability property for isometries from a normed space into a Banach space, in which the parallelogram law holds.

MSC:
39B82Stability, separation, extension, and related topics
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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References:
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