Approximate homomorphisms from ternary semigroups to modular spaces

Abstract

In this article, we investigate the generalized Hyers-Ulam stability of ternary homomorphisms from ternary semigroups into modular spaces. Ternary algebraic structures appear in theoretical and mathematical physics. We show the stability of that functional equation without 2-condition and Fatou property of the modular space. Moreover, we solve the same problem for -homogeneous Banach spaces and show a hyperstability of a mapping from ternary semigroups into normed algebras.