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An additive functional equation in orthogonality spaces
- Issue Date
- Jun-2012
- Publisher
- Springer-Verlag Berlin Heidelberg
- Citation
- Essays in Mathematics and its Applications: In Honor of Stephen Smale's 80th Birthday, v.9.78364E+12, pp.335 - 367
- Indexed
- SCOPUS
- Journal Title
- Essays in Mathematics and its Applications: In Honor of Stephen Smale's 80th Birthday
- Volume
- 9.78364E+12
- Start Page
- 335
- End Page
- 367
- ISSN
- 0000-0000
- Abstract
- By applying the fixed point method as well as the direct method, we provide a proof of the Hyers-Ulam stability of linear mappings, isometric linear mappings and 2-isometric linear mappings in Banach modules over a unital C ∗-algebra and in non-Archimedean Banach modules over a unital C ∗-algebra associated with an orthogonally additive functional equation. Moreover, we prove the Hyers-Ulam stability of homomorphisms in C ∗-algebras associated with an orthogonally additive functional equation.
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