# On approximate homomorphisms of ternary semigroups

Volume 10, Issue 8, pp 4071--4076 Publication Date: August 06, 2017

### 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

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