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 $$\Delta _2$$ -condition and Fatou property of the modular space. Moreover, we solve the same problem for $$\beta $$ -homogeneous Banach spaces and show a hyperstability of a mapping from ternary semigroups into normed algebras.