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http://dx.doi.org/10.4134/CKMS.2008.23.2.191

SOLUTION OF A VECTOR VARIABLE BI-ADDITIVE FUNCTIONAL EQUATION  

Park, Won-Gil (National Institute for Mathematical Sciences)
Bae, Jae-Hyeong (Department of Applied Mathematics Kyunghee University)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.2, 2008 , pp. 191-199 More about this Journal
Abstract
We investigate the relation between the vector variable bi-additive functional equation $f(\sum\limits^n_{i=1} xi,\;\sum\limits^n_{i=1} yj)={\sum\limits^n_{i=1}\sum\limits^n_ {j=1}f(x_i,y_j)$ and the multi-variable quadratic functional equation $$g(\sum\limits^n_{i=1}xi)\;+\;\sum\limits_{1{\leq}i<j{\leq}n}\;g(x_i-x_j)=n\sum\limits^n_{i=1}\;g(x_i)$$. Furthermore, we find out the general solution of the above two functional equations.
Keywords
solution; stability; vector variable bi-additive mapping;
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1 S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, 1968, p.63
2 J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge Univ. Press, Cambridge, 1989
3 J.-H. Bae and K.-W. Jun, On the generalized Hyers-Ulam-Rassias stability of an ndimensional quadratic functional equation, J. Math. Anal. Appl. 258 (2001), 183-193   DOI   ScienceOn
4 J.-H. Bae and W.-G. Park, On the generalized Hyers-Ulam-Rassias stability in Banach modules over a C-algebra, J. Math. Anal. Appl. 294 (2004), 196-205   DOI   ScienceOn
5 J.-H. Bae and W.-G. Park, On stability of a functional equation with n variables, Nonlinear Anal. 64 (2006), 856-868   DOI   ScienceOn
6 S.-M. Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl. 222 (1998), 126-137   DOI   ScienceOn
7 C.-G. Park, Cauchy-Rassias stability of a generalized Trif 's mapping in Banach modules and its applications, Nonlinear Anal. 62 (2005), 595-613   DOI   ScienceOn