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The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces. (English) Zbl 1446.39024

Summary: In this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation: \[ f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y), \] where \(f\) maps from an additive group to a complete non-Archimedean normed space.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B55 Orthogonal additivity and other conditional functional equations
39B82 Stability, separation, extension, and related topics for functional equations
47H10 Fixed-point theorems
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
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References:

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