ADDITIVE π-FUNCTIONAL EQUATIONS IN BANACH SPACES
6
μ‘°ν
0
λ€μ΄λ‘λ
0
μΈμ©
0
μ°Έκ³ λ¬Έν
ν€μλ
μ΄λ‘
In this paper, we solve the additive π-functional equations f(x+y+z)-f(x)-f(y)-f(z)= π(2f((x+y+z)/2)- f(x) - f(y)- f(z)), where π is a fixed number with π β 1, 2, and f(x+y+z)-f(x)-f(y)-f(z)=π(2f((x+y)/2)+z)- f(x) - f(y)- 2f(z)), where π is a fixed number with πβ 1. Using the direct method, we prove the Hyers-Ulam stability of the additive π-functional equations (0.1) and (0.2) in Banach spaces.
Abstract
In this paper, we solve the additive π-functional equations f(x+y+z)-f(x)-f(y)-f(z)= π(2f((x+y+z)/2)- f(x) - f(y)- f(z)), where π is a fixed number with π β 1, 2, and f(x+y+z)-f(x)-f(y)-f(z)=π(2f((x+y)/2)+z)- f(x) - f(y)- 2f(z)), where π is a fixed number with πβ 1. Using the direct method, we prove the Hyers-Ulam stability of the additive π-functional equations (0.1) and (0.2) in Banach spaces.
μ°Έκ³ λ¬Έν (5)
- T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
- P. Gavruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 184, pp.431~443 (1994)
- D.H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
- Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
- S.M. Ulam, "Collection of the Mathematical Problems" (1960), Interscience Publ