On Some Sequence Spaces via q-Pascal Matrix and Its Geometric Properties

Abstract

We develop some new sequence spaces l(p)(P(q)) and l(infinity)(P(q)) by using q-Pascal matrix P(q). We discuss some topological properties of the newly defined spaces, obtain the Schauder basis for the space l(p)(P(q)) and determine the Alpha-(alpha-), Beta-(beta-) and Gamma-(gamma-) duals of the newly defined spaces. We characterize a certain class (l(p)(P(q)),X) of infinite matrices, where X is an element of {l(infinity),c,c(0)}. Furthermore, utilizing the proposed results, we characterize certain other classes of infinite matrices. We also examine some geometric properties, like the approximation property, Dunford-Pettis property, Hahn-Banach extension property, and Banach-Saks-type p property of the spaces l(p)(P(q)) and l(infinity)(P(q)).