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A fixed point approach to the stability of functional equations in non-Archimedean metric spaces. (English) Zbl 1237.39022
Let X be an arbitrary set, Y be a complete ultrametric space, f 1 ,,f k :XX, Φ:X×Y k Y. The authors find conditions for the solvability of the functional equation Φ(x,ψ(f 1 (x)),,ψ(f k (x)))=ψ(x), xX (with respect to ψ:XY) and its generalizations. The result, in the spirit of the Hyers-Ulam stability where a solution is obtained as a limit of approximate solutions, is based on a new fixed point theorem.

MSC:
39B52Functional equations for functions with more general domains and/or ranges
39B82Stability, separation, extension, and related topics
54H25Fixed-point and coincidence theorems in topological spaces
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