• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.131-138
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• 2016

We determine the general solutions $f:\mathbb{R}^2{\rightarrow}\mathbb{R}$ of the functional equation f(ux-vy, uy+v(x+y)) = f(x, y)f(u, v) for all x, y, u, $v{\in}\mathbb{R}$. We also investigate both bounded and unbounded solutions of the functional inequality ${\mid}f(ux-vy,uy+v(x+y))-f(x,y)f(u,v){\mid}{\leq}{\phi}(u,v)$ for all x, y, u, $v{\in}\mathbb{R}$, where ${\ph}:\mathbb{R}^2{\rightarrow}\mathbb{R}_+$ is a given function.