• Title, Summary, Keyword: quasiadditive map

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ON THE STABILITY OF A JENSEN TYPE FUNCTIONAL EQUATION ON GROUPS

  • FAIZIEV VALERH A.;SAHOO PRASANNA K.
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.757-776
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    • 2005
  • In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).