Vahid Keshavarz, Ali lloon Kashkooly, Dalal Alhwikem, HU stability of i-F-hom-der on Banach algebras: Solutions and methods, Vol. 2026 (2026), No. 16, pp. 1- 10

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DOI: 10.23952/jnfa.2026.16

Received January 9, 2025; Accepted April 9, 2026; Published June 10, 2026

Abstract. In this paper, we define a new class of system of additive-quadratic functional equations on Banach algebras, which we call the system of $i$ -mappings, where $i \in \{1, 2\}.$ We introduce the notion of a $i$ – $\mathscr{F}$ -homomorphism-derivations (abbreviated $i$ – $\mathscr{F}$ -hom-ders), with $i \in \{1, 2\}:$ for $i = 1,~\mathscr{F}$ is a linear homomorphism, and for $i = 2,~f$ is a quadratic homomorphism on Banach algebras. Finally, using a fixed-point method, we investigate Hyers–Ulam stability for the system of additive-quadratic functional equations and $i$ – $\mathscr{F}$ -hom-ders, employing Gavruta-type, Rassias-type and JMRassias-type control functions on Banach algebras.

How to Cite this Article:
V. Keshavarz, A. lloon Kashkooly, D. Alhwikem, HU Stability of i-F-Hom-Der on Banach algebras: Solutions and methods, J. Nonlinear Funct. Anal. 2026 (2026) 16.