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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Let n ≥2 be an even integer. We investigate that if an odd mapping f:X →Y satisfies the following equation [수식]+[수식]=[수식] then f:X →Y is additive, where r ∈R. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C^*-algebras.
As an application, we show that every almost linear bijection h:A→B of unital C^*-algebras A and B is a C^*-algebra isomorphism when h[수식]=h[수식]h(y) for all unitaries u∈ A, all y∈ A, and s=0,1,2,.....
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참고문헌 (15)
참고문헌 신청
C. Baak / 2006 / Generalized additive mapping in Banach modules and isomorphisms between C*-algebras / J. Math. Anal. Appl 314 (1) : 150 ~ 161
D. H. Hyers / 1941 / On the stability of the linear functional equation / Proc. Nat. Acad. Sci. U.S.A : 222 ~ 224
F. Skof / 1983 / Local properties and approximation of operat / Rend. Sem. Mat. Fis. Milano 53 : 113 ~ 129
G.-L. Forti / 1995 / Hyers-Ulam stability of functional equations in several variables / Aequa-tiones Math 50 (1) : 143 ~ 190
G.-L. Forti / 2004 / Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations / J. Math. Anal. Appl 295 (1) : 127 ~ 133
D. H. Hyers / 1941 / On the stability of the linear functional equation / Proc. Nat. Acad. Sci. U.S.A : 222 ~ 224
F. Skof / 1983 / Local properties and approximation of operat / Rend. Sem. Mat. Fis. Milano 53 : 113 ~ 129
G.-L. Forti / 1995 / Hyers-Ulam stability of functional equations in several variables / Aequa-tiones Math 50 (1) : 143 ~ 190
G.-L. Forti / 2004 / Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations / J. Math. Anal. Appl 295 (1) : 127 ~ 133
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