On some classes of compact and matrix operators on the generalized weighted mean difference sequence spaces of fractional order

Recently, the generalized weighted mean difference operator of fractional order and related sequence spaces were introduced and studied by Nayak et al. (Proc Natl Acad Sci India Sect A Phys Sci 89(1):163-170, 2019). In this paper, some basic ideas on topological structures, inclusion relations and dual spaces of the defined spaces were discussed. Also, we discuss some results on matrix transformations and Hausdorff measure of noncompactness of those sequence spaces. The Hausdorff measures of noncompactness of the related operators that map an arbitrary BK-space into the classical sequence spaces are established. Furthermore, by using this measure, the characterizations of some classes of weighted mean compact operators are determined in the BK-spaces.