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A fixed point approach to the stability of an additive-quadratic-cubic-quartic functional equation. (English) Zbl 1187.39042
Summary: Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation \(f(x+2y)+f(x - 2y)=4f(x+y)+4f(x - y) - 6f(x)+f(2y)+f( - 2y) - 4f(y) - 4f( - y)\) in Banach spaces.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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