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

Document Type: Research Paper

Authors

1 Marand Branch, Islamic Azad University,

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}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =
(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}
f(x_{i}).
end{equation}

Keywords