Solution of a vector variable bi-additive functional equation

Commun. Korean Math. Soc. 2008 Vol. 23, No. 2, 191-199 Printed June 1, 2008

Won-Gil Park and Jae-Hyeong Bae National Institute for Mathematical Sciences and Kyunghee University

Abstract : We investigate the relation between the vector variable bi-additive functional equation $\displaystyle f\big(\sum_{i=1}^nx_i,\sum_{i=1}^ny_j\big) =\sum_{i=1}^n\sum_{j=1}^nf(x_i,y_j)$ and the multi-variable quadratic functional equation $$\displaystyle g\big(\sum_{i=1}^nx_i\big) +\sum_{1\le i