On stability problems with shadowing property and its application
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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,.....
Abstract
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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