학술저널
APPROXIMATELY ADDITIVE MAPPINGS OVER p-ADIC FIELDS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 21, No. 1
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2008.031 - 14 (14 pages)
- 0
In this paper, we prove the Hyers{Ulam{Rassias sta-bility of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation 2f( x+y2 ) = f(x) + f(y) over the p-adic ¯eld Qp. The concept of Hyers{Ulam{Rassias stability orig-inated 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.
1. Introduction and preliminaries
2. Stability of the Cauchy mapping over the p-adic ¯eld Qp
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