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Hyers-Ulam-Rassias stability of the Apollonius type quadratic mapping in non-Archimedean spaces. (English) Zbl 1170.39017
Using some ideas of M. S. Moslehian and T. M. Rassias [Appl. Anal. Disc. Math. 1, No. 2, 325–334 (2007)] the authors prove the Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type \(Q(z - x) + Q(z - y) = \frac{1}{2}Q(x - y) + 2Q (z - \frac{x + y}{2})\) in non-Archimedean spaces.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B22 Functional equations for real functions
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
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