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Ternary derivations, stability and physical aspects. (English) Zbl 1135.39014
The author states some various definitions of ternary structures [cf. M. S. Moslehian, Bull. Belg. Math. Soc. 14, No. 1, 135–142 (2007; Zbl 1132.39026), M. Amyari and M. S. Moslehian [Lett. Math. Phys. 77, No. 1, 1–9 (2006; Zbl 1112.39021)] and proves the generalized Hyers-Ulam-Rassias stability of ternary derivations associated with the generalized Jensen functional equation by using a fixed point method [see also M.S. Moslehian and L. Székelyhidi, Result. Math. 49, No. 3–4, 289–300 (2006; Zbl 1114.39010)]. Some examples of physical applications of ternary structures are given as well.

MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
17A40Ternary compositions
17A36Automorphisms, derivations, other operators
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