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- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 375 - 382 (8page)
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In this paper, we solve the additive 𝜌-functional equations f(x+y+z)-f(x)-f(y)-f(z)= 𝜌(2f((x+y+z)/2)- f(x) - f(y)- f(z)), where 𝜌 is a fixed number with 𝜌 ≠1, 2, and f(x+y+z)-f(x)-f(y)-f(z)=𝜌(2f((x+y)/2)+z)- f(x) - f(y)- 2f(z)), where 𝜌 is a fixed number with 𝜌≠1. Using the direct method, we prove the Hyers-Ulam stability of the additive 𝜌-functional equations (0.1) and (0.2) in Banach spaces.
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참고문헌 (5)
참고문헌 신청
D.H. Hyers / 1941 / On the stability of the linear functional equation / Proc. Natl. Acad. Sci. U.S.A 27 : 222 ~ 224
P. Gavruta / 1994 / A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings / J. Math. Anal. Appl 184 : 431 ~ 443
S.M. Ulam / 1960 / Collection of the Mathematical Problems / Interscience Publ
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2 : 64 ~ 66
Th.M. Rassias / 1978 / On the stability of the linear mapping in Banach spaces / Proc. Amer. Math. Soc 72 : 297 ~ 300
P. Gavruta / 1994 / A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings / J. Math. Anal. Appl 184 : 431 ~ 443
S.M. Ulam / 1960 / Collection of the Mathematical Problems / Interscience Publ
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2 : 64 ~ 66
Th.M. Rassias / 1978 / On the stability of the linear mapping in Banach spaces / Proc. Amer. Math. Soc 72 : 297 ~ 300
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