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A NOTE ON THE HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC EQUATION

  • Published : 2004.08.01

Abstract

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by (x * y) + (x * $y^{-1}$) - 2 (x) - 2 (y) =<${\varphi}$(x,y), (x*y*z)+ (x)+ (y)+ (z)- (x*y)- (y*z)- (z*x)=${\varphi}$(x, y, z), where (G,*) is a group, X is a real or complex Hausdorff topological vector space, and is a function from G into X.

Keywords

quadratic function

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Cited by

  1. Elementary remarks on Ulam–Hyers stability of linear functional equations vol.328, pp.1, 2007, https://doi.org/10.1016/j.jmaa.2006.04.079