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SOLUTION OF A VECTOR VARIABLE BI-ADDITIVE FUNCTIONAL EQUATION

  • Published : 2008.04.30

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

References

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  3. Remarks on the Hyers–Ulam stability of some systems of functional equations vol.219, pp.8, 2012, https://doi.org/10.1016/j.amc.2012.10.057
  4. On an equation characterizing multi-additive-quadratic mappings and its Hyers–Ulam stability vol.265, 2015, https://doi.org/10.1016/j.amc.2015.05.037
  5. On Stability and Hyperstability of an Equation Characterizing Multi-Cauchy–Jensen Mappings vol.73, pp.2, 2018, https://doi.org/10.1007/s00025-018-0815-8