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On a direct method for proving the Hyers-Ulam stability of functional equations. (English) Zbl 1198.39039
The author uses the direct method to investigate the stability of the functional equation
\[ f(x)=\alpha f(h(x))+\beta f(-h(x)), \] where \(f : X \to Y\) is a function from a nonempty set \(X\) with an involution into a Banach space \((Y ,\|.\|)\) under certain conditions on the real constants \(\alpha, \beta\) and the odd function \(h: X \to X\). She then nicely applies her results for obtaining several various stability results.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B55 Orthogonal additivity and other conditional functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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