Oresme Numbers and Associated BK-Sequence Spaces

The aim of this research is to present the formulation of a new conservative matrix operator containing non-integer Oresme numbers, to obtain new BK-sequence spaces with the help of domains of this matrix operator on the spaces of convergent and null sequences. In the continuation of study, inclusion relations, alpha, beta and gamma duals, Schauder basis and matrix mapping classes concerning these spaces are introduced. Finally, compact operators on these novel sequence spaces are characterized by the utilization of Hausdorff measure of non-compactness.