• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.515-523
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• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-709
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• 2006

Let X, Y be vector spaces. It is shown that if an even mapping $f:X{\rightarrow}Y$ satisfies f(0) = 0 and $$(0.1)\;f(\frac {x+y} 2+z)+f(\frac {x+y} 2-z)+f(\frac {x-y} 2+z)+f(\frac {x-y} 2-z)=f(x)+f(y)+4f(z)$$ for all x, y, z ${\in}$X, then the mapping $f:X{\rightarrow}Y$ is quadratic. Furthermore, we prove the Cauchy-Rassias stability of the functional equation (0.1) in Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.987-996
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• 2010

In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation: $$f(\frac{sx+ty}{2}+rz)+f(\frac{sx+ty}{2}-rz)+f(\frac{sx-ty}{2}+rz)+f(\frac{sx-ty}{2}-rz)=s^2f(x)+t^2f(y)+4r^2f(z)$$ for any fixed nonzero integers s, t, r with $r\;{\neq}\;{\pm}1$.