Cesaro sequence spaces via (p, q)-calculus and compact matrix operators

In this article, we construct (p, q)-analogue C(p, q) of Cesaro matrix C-1 of order 1 and study its properties. We introduce (p, q)-Cesaro sequence spaces chi(p,q)(s) and chi(p,q)(infinity) generated by the domain of matrix C(p, q) in the spaces l(s) and l(infinity), respectively. We study some topological properties and inclusion relations, obtain Schauder basis of chi(p,q)(s) and alpha-, beta- and gamma-duals of the spaces chi(p,q)(s) and chi(p,q)(infinity). We characterize matrix mappings from the spaces chi(p,q)(s) and chi(p,q)(infinity) space mu is an element of {l(infinity), c, c(0)}. Finally, we characterize certain classes of compact operators on the newly defined spaces using Hausdorff measure of non compactness.