Generalized Ternary Hom-Derivations and Jensen $\rho$-Functional Equation: Solving and Stability
DOI:
https://doi.org/10.30495/jme.v18i0.3092Keywords:
fixed point method, generalized ternary hom-derivations, stability.Abstract
In this research, we aim to present the concept of the new generalized Jensen $\rho$-functional equation. Next, by utilizing ternary homomorphisms and derivations, we define the new generalized ternary hom-derivations linked to this equation within ternary Banach algebras. We demonstrate that the generalized Jensen $\rho$-functional equation belongs to the category of additive functions. Furthermore, employing the fixed point theorem, we establish the stability of both the generalized Jensen $\rho$-functional equation and the associated generalized ternary hom-derivations, using control functions inspired by G$\check{a}$vruta and Rassias. Lastly, we investigate the Jordan property as it pertains to generalized ternary hom-derivations linked to this equation within ternary Banach algebras, alongside the generalized ternary (Jordan) hom-derivations can be stable.Downloads
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