학술저널
THE STABILITY OF LINEAR MAPPINGS IN BANACH MODULES ASSOCIATED WITH A GENERALIZED JENSEN MAPPING
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 24, No. 2
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2011.05287 - 301 (15 pages)
- 2
Let X and Y be vector spaces. It is shown that a mapping f : X ! Y satis es the functional equation if and only if the mapping f : X ! Y is Cauchy additive, and prove the Cauchy-Rassias stability of the functional equation (z) in Banach modules over a unital C-algebra. Let A and B be unital C-algebras. As an appli- cation, we show that every almost homomorphism h : A ! B of A into B is a homomorphism when h((k 􀀀 1)nuy) = h((k 􀀀 1)nu)h(y) for all unitaries u 2 A, all y 2 A, and n = 0; 1; 2; . Moreover, we prove the Cauchy-Rassias stability of homomorphisms in C-algebras.
1. Introduction
2. A generalized Jensen s mapping
3. Isomorphisms in unital C∗-algebras
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