Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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STABILITY OF TWO FUNCTIONAL EQUATIONS ARISING FROM DETERMINANT OF MATRICES

  • Choi, Chang-Kwon (Department of Mathematics Chonbuk National University) ;
  • Kim, Jongjin (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University) ;
  • Lee, Bogeun (Department of Mathematics Chonbuk National University)
  • Received : 2015.09.11
  • Published : 2016.07.31
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Abstract

Let $f:{\mathbb{R}}^3{\rightarrow}{\mathbb{R}}$. In this paper we prove the stability of functional inequalities ${\mid}f(ux+vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$, ${\mid}f(ux-vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$ for all $x,y,z,u,v,w{\in}{\mathbb{R}}$. Furthermore, we give refined descriptions of bounded functions satisfying the inequalities as in Albert and Baker [1].

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References

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