Abstract
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{eqnarray*} &&f\Big(\Big(\sum_{i=1}^{l}x_i\Big) +x_{l+1}\Big)+f\Big(\Big(\sum_{i=1}^{l}x_i\Big) -x_{l+1}\Big)+2\sum_{i=1}^{l}f(x_i)\\ &&\qquad \qquad =2f\Big(\sum_{i=1}^{l}x_i\Big)+\sum_{i=1}^{l}[f(x_i +x_{l+1})+f(x_i -x_{l+1})] \end{eqnarray*} for all $(x_1,\cdots,x_l, x_{l+1}) \in X^{l+1},$ where $l\ge 2.$
Citation
Kil-Woung Jun. Hark-Mahn Kim. "Ulam stability problem for a mixed type of cubic and additive functional equation." Bull. Belg. Math. Soc. Simon Stevin 13 (2) 271 - 285, June 2006. https://doi.org/10.36045/bbms/1148059462
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