In this paper we define the space c_o(Δ)={x=(x_k)/x_k−k_k−1→0(k→∞), x_o=0,x_k∈ℂ} and compute its duals (Continuous dual, β-dual and N-dual) The aim of this paper is to give same results about matrix mapping of c_o(Δ) into other sequence spaces including the convergent sequences, null sequences and bounded sequences.