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Solutions and Stability of Some Functional Equations on Semigroups

  • Keltouma Belfakih
  • Elhoucien Elqorachi
  • Themistocles M. RassiasEmail author
Chapter

Abstract

In this paper we investigate the solutions and the Hyers-Ulam stability of the μ-Jensen functional equation
$$\displaystyle f(xy)+\mu (y)f(x\sigma (y))=2f(x),\;x,y \in S, $$
a variant of the μ-Jensen functional equation
$$\displaystyle f(xy)+\mu (y)f(\sigma (y)x)=2f(x),\;x,y \in S, $$
and the μ-quadratic functional equation
$$\displaystyle f(xy)+\mu (y)f(x\sigma (y))=2f(x)+2f(y),\;x,y \in S, $$
where S is a semigroup, σ is a morphism of S and μ: \(S\longrightarrow \mathbb {C}\) is a multiplicative function such that μ((x)) = 1 for all x ∈ S.

Keywords

Functional equation Hyers-Ulam stability μ-Jensen functional equation μ-Quadratic functional equation 

Mathematics Subject Classification (2010)

Primary 49B82; Secondary 39C52 39C62 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Keltouma Belfakih
    • 1
  • Elhoucien Elqorachi
    • 1
  • Themistocles M. Rassias
    • 2
    Email author
  1. 1.Department of Mathematics, Faculty of SciencesUniversity Ibn ZohrAgadirMorocco
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece

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