A fixed point approach to orthogonal stability of an additive-cubic functional equation. (English) Zbl 1367.39005

Summary: Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-cubic functional equation \[ f(2x+y)+f(2x-y)-f(4x)=2f(x+y)+2f(x-y)-8f(2x)+10f(x)-2f(-x) \] for all \(x\), \(y\) with \(x \bot y\).


39B22 Functional equations for real functions
39B55 Orthogonal additivity and other conditional functional equations
39B82 Stability, separation, extension, and related topics for functional equations
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