Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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APPROXIMATELY ADDITIVE MAPPINGS OVER p-ADIC FIELDS

  • Park, Choonkil (Department of Mathematics Hanyang University) ;
  • Boo, Deok-Hoon (Department of Mathematics Chungnam National University) ;
  • Rassias, Themistocles M. (Department of Mathematics National Technical University of Athens Zografou Campus)
  • Received : 2007.07.16
  • Published : 2008.03.31
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Abstract

In this paper, we prove the Hyers-Ulam-Rassias stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation $2f(\frac{x+y}{2})=f(x)+f(y)$ over the p-adic field ${\mathbb{Q}}_p$. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

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Acknowledgement

Supported by : Chungnam National University