Measures of noncompactness in (N¯qΔ)summable difference sequence spaces

Abstract

In this paper we first introduceN q ∆ summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices A to map these sequence spaces into the spaces c, c 0 , and ∞. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.