# zbMATH — the first resource for mathematics

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