Articles

ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

  • Iz-iddine EL-FASSI ,
  • Janusz BRZDȨ ,
  • K ,
  • Abdellatif CHAHBI ,
  • Samir KABBAJ
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  • 1. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 133, Kenitra, Morocco;
    2. Department of Mathematics, Pedagogical University, Podchor??ych 2, 30-084 Kraków, Poland;
    3. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 133, Kenitra, Morocco

Received date: 2016-07-20

  Revised date: 2016-12-07

  Online published: 2017-12-25

Abstract

We present results on approximate solutions to the biadditive equation
f(x + y, z-w) + f(x-y, z + w)=2f(x, z)-2f(y, w)
on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.

Cite this article

Iz-iddine EL-FASSI , Janusz BRZDȨ , K , Abdellatif CHAHBI , Samir KABBAJ . ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J]. Acta mathematica scientia, Series B, 2017 , 37(6) : 1727 -1739 . DOI: 10.1016/S0252-9602(17)30103-0

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