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Zbl 1135.39014
Ternary derivations, stability and physical aspects.
(English)
[J] Acta Appl. Math. 100, No. 2, 187-199 (2008). ISSN 0167-8019; ISSN 1572-9036/e

The author states some various definitions of ternary structures [cf. {\it M. S. Moslehian}, Bull. Belg. Math. Soc. 14, No. 1, 135--142 (2007; Zbl 1132.39026), {\it M. Amyari} and {\it 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 {\it M.S. Moslehian} and {\it 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 2000:
*39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains
17A40 Ternary compositions
17A36 Automorphisms and other operators

Keywords: generalized Hyers-Ulam-Rassias stability; super stability; ternary algebra; tri-module; ternary derivation; generalized Jensen functional equation.

Citations: Zbl 1112.39021; Zbl 1114.39010; Zbl 1132.39026

Cited in: Zbl 1260.39034

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