SOLUTION OF A VECTOR VARIABLE BI-ADDITIVE FUNCTIONAL EQUATION

Title & Authors
SOLUTION OF A VECTOR VARIABLE BI-ADDITIVE FUNCTIONAL EQUATION
Park, Won-Gil; Bae, Jae-Hyeong;

Abstract
We investigate the relation between the vector variable bi-additive functional equation $\small{f(\sum\limits^n_{i=1} xi,\;\sum\limits^n_{i=1} yj)={\sum\limits^n_{i=1}\sum\limits^n_ {j=1}f(x_i,y_j)}$ and the multi-variable quadratic functional equation $\small{g(\sum\limits^n_{i=1}xi)\;+\;\sum\limits_{1{\leq}i}$<$\small{j{\leq}n}\;g(x_i-x_j)=n\sum\limits^n_{i=1}\;g(x_i)}$. Furthermore, we find out the general solution of the above two functional equations.
Keywords
Language
English
Cited by
1.
Stability of multi-additive mappings in -Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, 2012, 75, 11, 4205
2.
On an equation characterizing multi-cauchy-jensen mappings and its Hyers-Ulam stability, Acta Mathematica Scientia, 2015, 35, 6, 1349
3.
Remarks on the Hyers–Ulam stability of some systems of functional equations, Applied Mathematics and Computation, 2012, 219, 8, 4096
4.
On an equation characterizing multi-additive-quadratic mappings and its Hyers–Ulam stability, Applied Mathematics and Computation, 2015, 265, 448
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