Hyers–Ulam Stability of Wilson’s Functional Equation

Elhoucien Elqorachi (), Youssef Manar () and Themistocles M. Rassias ()
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Elhoucien Elqorachi: University Ibn Zohr, Department of Mathematics, Faculty of Sciences
Youssef Manar: University Ibn Zohr, Superior School of Technology
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics

A chapter in Contributions in Mathematics and Engineering, 2016, pp 165-183 from Springer

Abstract: Abstract Given a unitary character $$\mu: G \rightarrow \mathbf{C}$$ and an involution $$\sigma$$ of a group G, we study the Hyers–Ulam–Rassias stability of Wilson’s functional equations: $$\displaystyle\begin{array}{rcl} & f(xy) +\mu (y)f(x\sigma (y)) = 2f(x)g(y),\;x,y \in G,& {}\\ & f(xy) +\mu (y)f(x\sigma (y)) = 2g(x)f(y),\;x,y \in G.& {}\\ \end{array}$$ As a consequence, we find the superstability of d’Alembert’s functional equation: $$\displaystyle{g(xy) +\mu (y)g(x\sigma (y)) = 2g(x)g(y),\;x,y \in G.}$$

Keywords: Functional Equations; Hyers Ulam Rassias Stability; Superstrings; Unitary Character; Complex-valued Solutions (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31317-7_10

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DOI: 10.1007/978-3-319-31317-7_10

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