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On the Stability of Drygas Functional Equation on Amenable Semigroups

In: Handbook of Functional Equations

Author

Listed:
  • Elhoucien Elqorachi

    (University Ibn Zohr)

  • Youssef Manar

    (University Ibn Zohr)

  • Themistocles M. Rassias

    (National Technical University of Athens)

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

Suggested Citation

  • Elhoucien Elqorachi & Youssef Manar & Themistocles M. Rassias, 2014. "On the Stability of Drygas Functional Equation on Amenable Semigroups," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 135-154, Springer.
    • Handle: RePEc:spr:spochp:978-1-4939-1286-5_7
    DOI: 10.1007/978-1-4939-1286-5_7
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