Hyers–Ulam–Rassias Stability on Amenable Groups

Mohamed Akkouchi (), Elhoucien Elqorachi () and Khalil Sammad ()
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Mohamed Akkouchi: Cadi Ayyad University, Department of Mathematics, Faculty of Sciences Semlalia
Elhoucien Elqorachi: Ibn Zohr University, Department of Mathematics, Faculty of Sciences
Khalil Sammad: Ibn Tofail University, Department of Mathematics, Faculty of Sciences

A chapter in Contributions in Mathematics and Engineering, 2016, pp 377-392 from Springer

Abstract: Abstract In this chapter, we study the Ulam–Hyers–Rassias stability of the generalized cosine-sine functional equation: $$\displaystyle{\int _{K}\int _{G}f(xtk \cdot y)d\mu (t)dk = f(x)g(\,y) + h(\,y),\;x,y \in G,}$$ where f, g, and h 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 complex measure with compact support. Furthermore, we prove a stability theorem in the case where G is amenable, K is a finite subgroup of the automorphisms of G, and μ is a finite K-invariant complex measure, and we obtain also the Hyers–Ulam–Rassias stability of the generalized cosine-sine functional equation: $$\displaystyle{\,f(xy) + f(x\sigma (\,y)) = 2f(x)g(\,y) + 2h(\,y),x,y \in G,}$$ where G is amenable, $$\sigma$$ is an involution of G.

Keywords: Hyers Ulam Rassias Stability; Compact Subgroup; Functional Equations; Finite Subgroup; Normalized Haar Measure (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_19

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DOI: 10.1007/978-3-319-31317-7_19

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