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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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##### References:
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