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On the stability of the quadratic functional equation on bounded domains

Abstract

A result of Skof and Terracini will be generalized; More precisely, we will prove that if a functionf : [-t, t]nE satisfies the inequality (1) for some δ > 0 and for allx, y ∈ [-t, t]n withx + y, x - y ∈ [-t, t]n, then there exists a quadratic functionq: ℝnE such that ∥f(x) -q(x)∥ < (2912n2 + 1872n + 334)δ for anyx ∈ [-t, t]n.

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Correspondence to Soon-Mo Jung or Byungbae Kim.

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Jung, S., Kim, B. On the stability of the quadratic functional equation on bounded domains. Abh.Math.Semin.Univ.Hambg. 69, 293 (1999). https://doi.org/10.1007/BF02940881

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Key words and phrases

  • Hyers-Ulam stability
  • quadratic equation