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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.

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
Full Text: DOI
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