Matrix transformation and application of Hausdorff measure of non-compactness on newly defined Fibo-Pascal sequence spaces

Abstract

In this article, we introduce Fibo-Pascal sequence spaces P_{c}^{F}and P₀^{F} by utilizing a newly defined Fibo-Pascal matrix P^{F}. It is proved that P_{c}^{F}and P₀^{F} are BK-spaces that are linearly isomorphic to c and c₀, respectively. Furthermore, the Schauder basis and α-, β-, γ-duals of both the spaces are computed, and certain classes of matrix mappings are characterized. The final section is devoted to characterize compact operator on the space P₀^{F} via Hausdorff measure of non-compactness (shortly, HMNC).