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A fixed point approach to the stability of the cubic functional equation. (English) Zbl 1133.39028
Summary: L. Cădariu and V. Radu [JIPAM, J. Inequal. Pure Appl. Math. 4, No. 1, Paper No. 4 (2003; Zbl 1043.39010); Grazer Math. Ber. 346, 43–52 (2004; Zbl 1060.39028)] applied the fixed point method to the investigation of the Cauchy and Jensen functional equations. In this paper, we will adapt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of the cubic functional equation for a large class of functions from a vector space into a complete \(\beta\)-normed space.

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