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 Approximation of Cauchy additive mappings Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 851-860 Published online December 1, 2007 Jaiok Roh and Hui Joung Shin Hallym University, Chungnam National University Abstract : In this paper, we prove that a function satisfying the following inequality $${\parallel f(x) + 2f(y)+ 2f(z)\parallel} \le {\parallel 2 f(\frac{x}{2}+y+z)\parallel} + \epsilon ({\parallel x\parallel}^r \cdot {\parallel y\parallel}^r \cdot {\parallel z\parallel}^r)$$ for all $x, y, z \in X$ and for $\epsilon \ge 0$, is Cauchy additive. Moreover, we will investigate for the stability in Banach spaces. Keywords : Hyers-Ulam stability, Cauchy additive mapping, Jordan-von Neumann type Cauchy Jensen functional equation MSC numbers : Primary: 39B52, 39B62, 39B72 Downloads: Full-text PDF