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On the Stability of Drygas Functional Equation on Amenable Semigroups

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Handbook of Functional Equations

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 96))

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., \(|f(xy)-f(yx)|\leq\delta\)).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco

    Elhoucien Elqorachi & Youssef Manar

  2. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Themistocles M. Rassias

Authors
  1. Elhoucien Elqorachi
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  2. Youssef Manar
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  3. Themistocles M. Rassias
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Corresponding author

Correspondence to Youssef Manar .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Elqorachi, E., Manar, Y., Rassias, T. (2014). On the Stability of Drygas Functional Equation on Amenable Semigroups. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 96. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1286-5_7

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