Solution and stability of a cubic functional equation. (English) Zbl 1201.39024

Similar to the method used by H.-Y Chu and D.-S. Kang [J. Math. Anal. Appl. 325, No. 1, 595–607 (2007; Zbl 1106.39025)] and A. Najati and 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.


39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
Full Text: DOI


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