A Note on the Functions that Are Approximately p-Wright Affine

Janusz Brzdȩk ()
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Janusz Brzdȩk: Pedagogical University

A chapter in Handbook of Functional Equations, 2014, pp 43-55 from Springer

Abstract: Abstract Let W be a Banach space, $(V,+)$ be a commutative group, p be an endomorphism of V, and $\overline{p}:V\to V$ be defined by $\overline{p}(x):=x-p(x)$ for $x\in V$ . We present some results on the Hyers–Ulam type stability for the following functional equation $$f(p(x)+\overline{p}(x))+f(\overline{p}(x)+p(y))=f(x)+f(y),$$ in the class of functions $f:V\to W$ .

Keywords: Hyers–Ulam stability; p-Wright affine function; Polynomial function (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_3

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DOI: 10.1007/978-1-4939-1246-9_3

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