Document Type : Research Paper

Authors

• Sattar Alizadeh ¹
• Fridoun Moradlou ²

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:
$$\sum _{j=1}^{n}f(-2x_j+\sum _{i=1,\ne j}^n{x}_i)=(n-6)f(\sum _{i=1}^n{x}_i)+9\sum _{i=1}^{n}f(x_i).$$

Keywords

• Fixed point method, Hyers-Ulam-Rassias stability
• Multi-Banach spaces, Quadratic mapping