Hyers–Ulam–Rassias Stability of the Generalized Wilson’s Functional Equation

Elqorachi Elhoucien (), Youssef Manar () and Sammad Khalil ()
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Elqorachi Elhoucien: Ibn Zohr University
Youssef Manar: Ibn Zohr University
Sammad Khalil: Ibn Tofail University

A chapter in Mathematical Analysis, Approximation Theory and Their Applications, 2016, pp 219-233 from Springer

Abstract: Abstract In this chapter, we apply the fixed point theorem and the direct method to the proof of Hyers–Ulam–Rassias stability property for generalized Wilson’s functional equation ∫ K ∫ G f ( x t k . y ) d k d μ ( t ) = f ( x ) g ( y ) , x , y ∈ G , $$\displaystyle\begin{array}{rcl} \int _{K}\int _{G}f(xtk.y)dkd\mu (t) = f(x)g(y),\;x,y \in G,& & {}\\ \end{array}$$ where f, g are continuous complex valued functions on a locally compact group G, K is a compact subgroup of morphisms of G, dk is the normalized Haar measure on K and μ is a K-invariant complex measure with compact support.

Keywords: Banach space; Complex measure; Fixed point; Hyers-Ulam-Rassias stability; Locally compact group; Wilson’s functional equation (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31281-1_9

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DOI: 10.1007/978-3-319-31281-1_9

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