• Superstability of the generalized orthogonality equation on restricted domains

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/114/03/0253-0267

    • 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

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.