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
https://doi.org/10.4134/BKMS.2010.47.5.987
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
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd