FUNCTIONAL EQUATIONS IN THREE VARIABLES

• 발행기관: 충청수학회
• 저자명: Deok-Hoon Boo Chun-Gil Park Hee-Jung We
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 17, No. 2, 1~23쪽, 전체 23쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2004.10.30

영문 초록

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.

목차

1. Introduction

2. Functional equations in three variables

3. Stability of functional equations in three variables