# On approximate homomorphisms of ternary semigroups

Volume 10, Issue 8, pp 4071--4076 Publication Date: August 06, 2017       Article History
• 407 Views

### Authors

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

### Abstract

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.

### Keywords

• Ulam stability
• (commutative) ternary semigroup
• ternary homomorphism
• n-Banach space
• (complete) non-Archimedean normed space

•  12J25
•  17A40
•  39B52
•  39B82

### References

• [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., 248 (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.