(untitled) (European Journal of Pure and Applied Mathematics, 2026)
We introduce Γ_Δ-BE-algebras as a generalization of Γα- and Γ(α,β)-BE-algebras, and specify the algebraic conditions that govern this new structure. We investigate their fundamental properties, define the notions of ∆-subalgebras and ∆-filters, and examine their interrelations. Furthermore, we explore the behavior of two types of upper sets, E_α(x) and E^β_α(x, y), within the framework of ∆-left distributive Γ∆-BE-algebras, providing several characterizations and structural results. These findings offer a broadened perspective on algebraic systems related to BE-algebras and their logical extensions.