Solution and stability of a cubic functional equation
Similar to the method used by \textit{H.-Y Chu} and \textit{D.-S. Kang} [J. Math. Anal. Appl. 325, No.~1, 595--607 (2007; Zbl 1106.39025)] and \textit{A. Najati} and \textit{Ch. Park} [Acta Math. Sin., Engl. Ser. 24, No.~12, 1953--1964 (2008; Zbl 1159.39014)], the authors obtain the general solution and investigate the stability of the following cubic functional equation \[ f(x+ny)+f(x-ny)+f(nx)=n^2f(x+y)+n^2f(x-y)+(n^3-2n^2+2)f(x), \] where \(n\geq 2\) is an integer and \(f\) is a map between real vector spaces. They also investigate the stability of the equation above by using the fixed point method.
scientific article; zbMATH DE number 5790099