An Additive Functional Equation in Orthogonality Spaces

Choonkil Park () and Themistocles M. Rassias ()
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Choonkil Park: Hanyang University, Department of Mathematics, Research Institute for Natural Sciences
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics

A chapter in Essays in Mathematics and its Applications, 2012, pp 335-367 from Springer

Abstract: 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.

Keywords: Banach Modules; Hyers Ulam Stability; Isometric Linear Mappings; Fixed Point Method; Birkhoff-James Orthogonality (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-28821-0_14

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DOI: 10.1007/978-3-642-28821-0_14

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