Ulam stability problem for a mixed type of cubic and additive functional equation
Jun, Kil-Woung ; Kim, Hark-Mahn
Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, p. 271-285 / Harvested from Project Euclid
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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 $l\ge 2.$
Publié le : 2006-06-14
Classification:  Hyers-Ulam stability,  cubic mapping,  Banach module,  39A11,  39B72 
@article{1148059462,
     author = {Jun, Kil-Woung and Kim, Hark-Mahn},
     title = {Ulam stability problem for a mixed type of cubic and additive functional
equation},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {12},
     number = {5},
     year = {2006},
     pages = { 271-285},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148059462}
}

Jun, Kil-Woung; Kim, Hark-Mahn. Ulam stability problem for a mixed type of cubic and additive functional
equation. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp.  271-285. http://gdmltest.u-ga.fr/item/1148059462/