ABSTRACT: The sequence space V∞(θ) through the concept of invariant means and lacunary sequence space θ= (kr), have recently been introduced by Mursaleen (M. Mursaleen, Some matrix transformation on sequence spaces of invariant means, Hacettepe J. Math. Stat., 38(3)(2009): 259-264)), which was further studied by Ganie and Sheikh . In the present paper, our aim is to introduce and study V∞(f,θ) and V∞(f,p,θ), where f is a modulus function. We establish some inclusion relations between these spaces.