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Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces. (English) Zbl 1280.39019
Summary: Using the fixed point method, we investigate the Hyers-Ulam stability of a system of additive-cubic-quartic functional equations with constant coefficients in non-Archimedean 2-normed spaces. Also, we give an example to show that some results in the stability of functional equations in (Archimedean) normed spaces are not valid in non-Archimedean normed spaces.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B72 Systems of functional equations and inequalities
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
39B52 Functional equations for functions with more general domains and/or ranges
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