APPROXIMATELY ADDITIVE MAPPINGS OVER p-ADIC FIELDS

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 ( x+y 2 ) = f (x) + f (y) over the p-adic field Qp. 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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