SOME NEW SEQUENCE SPACES DEFINED BY MODULUS FUNCTION

Abstract

The main object of this paper is to introduce the sequence spaces [ \hat{V}, λ, f, p]_0 (Δ^r, E),  [ \hat{V}, λ, f, p]_1 (Δ^r, E), [ \hat{V}, λ, f, p]_∞(Δ^r, E), \hat{S}_λ (Δ^r, E) and \hat{S}_{λ_0} (Δ^r, E) where E is a Banach space which arise from the notion of generalized de la Vellee Poussin means andthe concept of modulus function, examine them and give various properties and inclusionrelations on these spaces.