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Superstability of the generalized orthogonality equation on restricted domains

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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: LetD n be a suitable subset of ℝn. If a function f:D n → 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 ∈ D n, thenf satisfies the generalized orthogonality equation for anyx, y ∈ D n.

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Authors and Affiliations

  1. Mathematics Section, College of Science and Technology, Hong-Ik University, 339-701, Chochiwon, Korea

    Soon-Mo Jung & Prasanna K. Sahoo

  2. Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA

    Prasanna K. Sahoo

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  1. Soon-Mo Jung
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  2. Prasanna K. Sahoo
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Jung, SM., Sahoo, P.K. Superstability of the generalized orthogonality equation on restricted domains. Proc Math Sci 114, 253–267 (2004). https://doi.org/10.1007/BF02830003

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  • DOI: https://doi.org/10.1007/BF02830003

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