Approximate a quadratic mapping in multi-Banach spaces, a fixed point approach

Document Type : Research Paper

Authors

1 Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran

2 Department of Mathematics, Sahand University of Technology, Tabriz, Iran

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:
\begin{equation}
\sum_{ j = 1}^{n}f\Big(-2 x_{j} + \sum_{ i = 1, \neq j}^{n} x_{i}\Big) =
(n-6) f\Big(\sum_{ i = 1}^{n} x_{i}\Big) + 9 \sum_{ i = 1}^{n}
f(x_{i}).
\end{equation}

Keywords