%0 Journal Article
%T Approximation of an additive mapping in various normed spaces
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Shiri, M. S.
%A Azadi Kenary, H.
%D 2015
%\ 10/01/2015
%V 41
%N 5
%P 1213-1233
%! Approximation of an additive mapping in various normed spaces
%K Hyers-Ulam-Rassias stability
%K non-Archimedean normed spaces
%K random normed spaces
%R
%X In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from 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.
%U http://bims.iranjournals.ir/article_686_ef1ccfb37f5b6e7b4200e921fa0b1fdd.pdf