A study on q-analogue of generalized Motzkin sequence spaces, their matrix transformations and compact operators

In this article, we have constructed generalized q-difference Motzkin sequence spaces [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] by composing q-Motzkin matrix with generalized q-difference matrix in the spaces [Formula: see text], respectively and explore their topological properties. We determine the bases for [Formula: see text] and [Formula: see text] and compute α-, β- and γ-duals of the newly defined spaces. Further, we characterize some class of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to the spaces [Formula: see text]. Lastly, compact operators are characterized on the spaces [Formula: see text] using Hausdorff measure of noncompactness.