A fixed point theorem and the Hyers-Ulam stability in non-Archimedean spaces. (English) Zbl 1286.47049

In this paper, a fixed point theorem in complete non-Archimedean normed space is proved. As an application, the Hyers-Ulam stability of some functional equations is proved. Examples are provided for Hyers-Ulam stability of functional equations in several variables.


47S10 Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory
47H10 Fixed-point theorems
39B82 Stability, separation, extension, and related topics for functional equations
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