On the Stability of Drygas Functional Equation on Amenable Semigroups

Elhoucien Elqorachi (), Youssef Manar () and Themistocles M. Rassias ()
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Elhoucien Elqorachi: University Ibn Zohr
Youssef Manar: University Ibn Zohr
Themistocles M. Rassias: National Technical University of Athens

A chapter in Handbook of Functional Equations, 2014, pp 135-154 from Springer

Abstract: Abstract In this chapter, we will prove the Hyers–Ulam stability of Drygas functional equation $$f(xy)+f(x\sigma(y))=2~f(x)+f(y)+f(\sigma(y)),\;x,y\in{G},$$ where G is an amenable semigroup, σ is an involution of G and $f:G\rightarrow E$ is approximatively central (i.e., $|f(xy)-f(yx)|\leq\delta$ ).

Keywords: Hyers–Ulam stability; Drygas functional equation; Amenable semigroups; Invariant means; Semigroups; Abelian groups (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1286-5_7

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DOI: 10.1007/978-1-4939-1286-5_7

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