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A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS

  • Park, Choon-Kil (DEPARTMENT OF MATHEMATICS RESEARCH INSTITUTE FOR NATURAL SCIENCES HANYANG UNIVERSITY) ;
  • Gordji, M. Eshaghi (DEPARTMENT OF MATHEMATICS SEMNAN UNIVERSITY) ;
  • Khodaei, H. (DEPARTMENT OF MATHEMATICS SEMNAN UNIVERSITY)
  • Received : 2009.03.24
  • Published : 2010.09.30

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 $r\;{\neq}\;{\pm}1$.

Acknowledgement

Supported by : National Research Foundation of Korea

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