Jun, Kil-Woung; Kim, Hark-Mahn Ulam stability problem for a mixed type of cubic and additive functional equation. (English) Zbl 1132.39022 Bull. Belg. Math. Soc. - Simon Stevin 13, No. 2, 271-285 (2006). Summary: It is the aim of this paper to obtain the generalized Hyers-Ulam stability result for a mixed type of cubic and additive functional equation\[ \begin{split} f\biggl(\biggl( \sum_{i=1}^l x_i\biggr)+ x_{x+1}\biggr)+ f\biggl(\biggl( \sum_{i=1}^l x_i\biggr)- x_{l+1}\biggr)+ 2\sum_{i=1}^l f(x_i)\\ =2f \biggl( \sum_{i=1}^l x_i\biggr)+ \sum_{i=1}^l [f(x_i+x_{l+1})+ f(x_i-x_{l+1})] \end{split} \]for all \((x_1,\dots, x_l,x_{l+1})\in X^{l+1}\), where \(l\geq 2\). Cited in 1 ReviewCited in 15 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges Keywords:cubic functional equation; Hyers-Ulam stability; cubic mapping; Banach module; additive functional equation PDFBibTeX XMLCite \textit{K.-W. Jun} and \textit{H.-M. Kim}, Bull. Belg. Math. Soc. - Simon Stevin 13, No. 2, 271--285 (2006; Zbl 1132.39022)