1
Department of Mathematics, Arsanjan Branch, Islamic Azad University, Arsanjan, Iran.
2
Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75918-74831, Iran.
Abstract
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.
Shiri,M. S. and Azadi Kenary,H. (2015). Approximation of an additive mapping in various normed spaces. Bulletin of the Iranian Mathematical Society, 41(5), 1213-1233.
MLA
Shiri,M. S. , and Azadi Kenary,H. . "Approximation of an additive mapping in various normed spaces", Bulletin of the Iranian Mathematical Society, 41, 5, 2015, 1213-1233.
HARVARD
Shiri M. S., Azadi Kenary H. (2015). 'Approximation of an additive mapping in various normed spaces', Bulletin of the Iranian Mathematical Society, 41(5), pp. 1213-1233.
CHICAGO
M. S. Shiri and H. Azadi Kenary, "Approximation of an additive mapping in various normed spaces," Bulletin of the Iranian Mathematical Society, 41 5 (2015): 1213-1233,
VANCOUVER
Shiri M. S., Azadi Kenary H. Approximation of an additive mapping in various normed spaces. BIMS, 2015; 41(5): 1213-1233.
