A fixed point approach to the Cauchy-Rassias stability of general Jensen type quadratic-quadratic mappings

Choonkil Park; M. Eshaghi Gordji; H. Khodaei

doi:10.4134/BKMS.2010.47.5.987

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(5): 987-996

Printed September 1, 2010

https://doi.org/10.4134/BKMS.2010.47.5.987

A fixed point approach to the Cauchy-Rassias stability of general Jensen type quadratic-quadratic mappings

Choonkil Park, M. Eshaghi Gordji, and H. Khodaei

Hanyang University, Semnan University, Semnan University

Abstract

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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