학술저널
FUNCTIONAL EQUATIONS IN THREE VARIABLES
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 17, No. 2
-
2004.101 - 23 (23 pages)
- 0
Let r, s be nonzero real numbers. Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f(0) = 0, and sf( x + y ± z r )+f(x)+f(y)±f (z) = sf( x + y r )+sf( y ± z r )+sf( x ± z r ), or sf( x + y ± z r ) + f(x) + f(y) ± f(z) = f(x + y) + f(y ± z) + f(x ± z) for all x, y, z ∈ X, then there exist an additive mapping A : X → Y and a quadratic mapping Q : X → Y such that f(x) = A(x) + Q(x) for all x ∈ X. Furthermore, we prove the Cauchy–Rassias stability of the functional equations as given above.
1. Introduction
2. Functional equations in three variables
3. Stability of functional equations in three variables
(0)
(0)