β , θ , ∂ , I ) - Continuous Mappings and their Decomposition

In this paper we introduce the concept of (α, β, θ, ∂, I)-continuous mappings and prove that if α, β are operators on the topological space (X, τ) and θ, θ∗ , ∂ are operators on the topological space (Y, φ) and I a proper ideal on X, then a function f : X → Y is (α, β, θ ∧ θ∗, ∂, I)-continuous if and only if it is both (α, β, θ, ∂, I) -continuous and (α, β, θ∗, ∂, I)-continuous, generalizing a result of J. Tong. Additional results on (α, Int, θ, ∂, {∅})-continuous maps are given.