**Volume 10, Issue 8, pp 4071--4076**

**Publication Date**: 2017-08-06

http://dx.doi.org/10.22436/jnsa.010.08.03

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.

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