Journal of the Orissa Mathematical Society Volume 30,No.2(2011),p.67-80 On Certain Summable Difference Sequence Spaces Generated by Infinite Matrices P. Baliarsingh and S. Dutta Department of Mathematics, Trident Academy of Technology, Infocity, Bhubaneswar -751024, India, Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, India, Abstract The main purpose of the this paper is to define certain kind of (C, 1), (V,λ)- summable difference sequence spaces [C, 1]( ˆ A, Δ r ν ,p), (C, 1)( ˆ A, Δ r ν ,p), [V,λ]( ˆ A, Δ r ν ,p) and (V,λ)( ˆ A, Δ r ν ,p) generated by infinite matrices. Also we discuss some results concerning their topological structures and some inclusion relations. Moreover we establish certain interesting results by introducing Orlicz functions on these spaces and determine their duals. Keywords : Difference operator; Orlicz function; Dual spaces. 2010 Mathematics Subject Classification : 40A05; 40C05; 46A45. 1 Introduction By ω, we denote the space of all scalar sequences and any subspace of ω is called a sequence space. Also by ℓ ∞ ,c and c 0 , we shall write the spaces of all bounded, convergent and null sequences with complex terms respectively, normed by ‖x‖ ∞ = sup k |x k | where k ∈ N = {1, 2, 3...}, the set of positive integers. The concept of difference sequence space was initially introduced by Kızmaz [1] and later on it has been studied and extended by many researchers (see [2-5]). The generalized de la Vallee- Poussin mean is defined by t n (x)= 1 λ n  k∈In x k (1.1) 67