We define the sequence spaces [ w θ , M , p , u , Δ ] σ , [ w θ , M , p , u , Δ ] σ 0 , and [ w θ , M , p , u , Δ ] σ ∞ which are defined by combining the concepts of Orlicz functions, invariant means, and lacunary convergence. We also study some inclusion relations and linearity properties of the above-mentioned spaces. These are generalizations of those defined and studied by Savaş and Rhoades in 2002 and some others before.