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http://dx.doi.org/10.4134/BKMS.2006.43.4.703

JENSEN TYPE QUADRATIC-QUADRATIC MAPPING IN BANACH SPACES  

Park, Choon-Kil (DEPARTMENT OF MATHEMATICS, HANYANG UNIVERSITY)
Hong, Seong-Ki (DEPARTMENT OF MATHEMATICS, CHUNGNAM NATIONAL UNIVERSITY)
Kim, Myoung-Jung (DEPARTMENT OF MATHEMATICS, CHUNGNAM NATIONAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.4, 2006 , pp. 703-709 More about this Journal
Abstract
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.
Keywords
Cauchy-Rassias stability; quadratic mapping; functional equation;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By SCOPUS : 1
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