한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)
- 제13권4호
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- Pages.295-301
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- 2006
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
ON THE SOLUTION OF A MULTI-VARIABLE BI-ADDITIVE FUNCTIONAL EQUATION I
- Park, Won-Gil (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES) ;
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Bae, Jae-Hyeong
(DEPARTMENT OF MATHEMATICAL AND APPLIED MATHEMATICS, KYUNG HEE UNIVERSITY)
- 발행 : 2006.11.30
초록
We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.