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.
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Park, C., Rassias, J.M., Bodaghi, A. et al. Approximate homomorphisms from ternary semigroups to modular spaces. RACSAM 113, 2175–2188 (2019). https://doi.org/10.1007/s13398-018-0608-7
- Generalized Hyers–Ulam stability
- Ternary homomorphism
- Modular space
- \(\Delta _2\)-condition
- Fatou property
- \(\beta \)-homogeneous Banach space
Mathematics Subject Classification
- Primary 17A40