Bulletin of the Belgian Mathematical Society - Simon Stevin

Ulam stability problem for a mixed type of cubic and additive functional equation

Kil-Woung Jun and Hark-Mahn Kim

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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 $l\ge 2.$

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 2 (2006), 271-285.

Dates
First available in Project Euclid: 19 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1148059462

Mathematical Reviews number (MathSciNet)
MR2259906

Zentralblatt MATH identifier
1132.39022

Subjects
Primary: 39A11 39B72: Systems of functional equations and inequalities

Keywords
Hyers-Ulam stability cubic mapping Banach module

Citation

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 13 (2006), no. 2, 271--285. https://projecteuclid.org/euclid.bbms/1148059462


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