On approximate homomorphisms of ternary semigroups

Volume 10, Issue 8, pp 4071--4076

Publication Date: 2017-08-06



Krzysztof Ciepliński - AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland.


We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into \(n\)-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and \(p\)-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists for their research in some problems coming from quantum physics, \(p\)-adic strings and superstrings.


Ulam stability, (commutative) ternary semigroup, ternary homomorphism, n-Banach space, (complete) non-Archimedean normed space, p-adic numbers.


[1] M. Amyari, M. S. Moslehian, Approximate homomorphisms of ternary semigroups, Lett. Math. Phys., 77 (2006), 1–9.
[2] N. Bazunova, A. Borowiec, R. Kerner, Universal differential calculus on ternary algebras, Lett. Math. Phys., 67 (2004), 195–206.
[3] N. Brillouët-Belluot, J. Brzdęk, K. Ciepliński, On some recent developments in Ulam’s type stability, Abstr. Appl. Anal., 2012 (2012), 41 pages.
[4] H.-Y. Chu, A. Kim, J. Park, On the Hyers-Ulam stabilities of functional equations on n-Banach spaces, Math. Nachr., 289 (2016), 1177–1188.
[5] H. Dutta, On some n-normed linear space valued difference sequences, J. Franklin Inst., 348 (2011), 2876–2883.
[6] G. P. Gehér, On n-norm preservers and the Aleksandrov conservative n-distance problem, ArXiv, 2015 (2015), 9 pages.
[7] H. Gunawan, M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631–639.
[8] S.-M. Jung, Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, Springer Science and Business Media, New York, (2011).
[9] R. Kerner, Ternary and non-associative structures, Int. J. Geom. Methods Mod. Phys., 5 (2008), 1265–1294.
[10] A. Khrennikov, Non-Archimedean analysis: quantum paradoxes, dynamical systems and biological models, Kluwer Academic Publishers, Dordrecht, (1997).
[11] Y. Ma, The Aleksandrov-Benz-Rassias problem on linear n-normed spaces, Monatsh. Math., 180 (2016), 305–316.
[12] A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299–319.
[13] M. S. Moslehian, Ternary derivations, stability and physical aspects, Acta Appl. Math., 100 (2008), 187–199.
[14] M. S. Moslehian, T. M. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math., 1 (2007), 325–334.
[15] C. Park, M. E. Gordji, Comment on ”Approximate ternary Jordan derivations on Banach ternary algebras” [Bavand Savadkouhi et al. J. Math. Phys. 50, 042303 (2009)], J. Math. Phys., 2010 (2010), 7 pages.
[16] J. M. Rassias, H.-M. Kim, Approximate homomorphisms and derivations between \(C^*\)-ternary algebras, J. Math. Phys., 2008 (2008), 10 pages.
[17] M. L. Santiago, S. Sri Bala, Ternary semigroups, Semigroup Forum, 81 (2010), 380–388.
[18] T. Z. Xu, Stability of multi-Jensen mappings in non-Archimedean normed spaces, J. Math. Phys., 2012 (2012), 9 pages.
[19] T. Z. Xu, J. M. Rassias, On the Hyers-Ulam stability of a general mixed additive and cubic functional equation in n-Banach spaces, Abstr. Appl. Anal., 2012 (2012), 23 pages.


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