• Superstability of the generalized orthogonality equation on restricted domains

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    • Keywords


      Superstability; generalized orthogonality equation

    • Abstract


      Chmielinski has proved in the paper [4] the superstability of the generalized orthogonality equation ¦〈f(x), f(y)〉¦ = ¦〈x,y〉¦. In this paper, we will extend the result of Chmielinski by proving a theorem: LetDn be a suitable subset of ℝn. If a function f:Dn → ℝn satisfies the inequality ∥〈f(x), f(y)〉¦ ¦〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ Dn, thenf satisfies the generalized orthogonality equation for anyx, y ∈ Dn.

    • Author Affiliations


      Soon-Mo Jung1 Prasanna K Sahoo1 2

      1. Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon - 339-701, Korea
      2. Department of Mathematics, University of Louisville, Louisville, KY - 40292, USA
    • Dates

  • Proceedings – Mathematical Sciences | News

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