Abstract
Ternary algebras and modules are vector spaces on which products of three factors are defined. In this paper, we present several physical applications of ternary structures. Some recent results on the stability of ternary derivations are reviewed. Using a fixed point method, we also establish the generalized Hyers–Ulam–Rassias stability of ternary derivations from a normed ternary algebra into a Banach tri-module associated to the generalized Jensen functional equations and prove a superstability result.
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The author was in part supported by a grant from IPM (No. 85390031).
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Moslehian, M.S. Ternary Derivations, Stability and Physical Aspects. Acta Appl Math 100, 187–199 (2008). https://doi.org/10.1007/s10440-007-9179-x
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DOI: https://doi.org/10.1007/s10440-007-9179-x
Keywords
- Generalized Hyers–Ulam–Rassias stability
- Superstability
- Ternary algebra
- Tri-module
- Ternary derivation
- Generalized Jensen functional equation