A fixed point approach to the Cauchy-Rassias stability of general Jensen type quadratic-quadratic mappings
Bull. Korean Math. Soc. 2010 Vol. 47, No. 5, 987-996
Published online September 1, 2010
Choonkil Park, M. Eshaghi Gordji, and H. Khodaei
Hanyang University, Semnan University, Semnan University
Abstract : 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 $r\neq \pm1$.
Keywords : Cauchy-Rassias stability, quadratic mapping, fixed point method
MSC numbers : 39B82, 39B52, 47H10
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