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

Abstract

In this article, we have constructed generalized q-difference Motzkin sequence spaces M0q(Δqm), Mcq(Δqm), Mpq(Δqm) and M∞q(Δqm) by composing q-Motzkin matrix with generalized q-difference matrix in the spaces c0,c,lp,l∞, respectively and explore their topological properties. We determine the bases for Mcq(Δqm) and M0q(Δqm) and compute α-, β- and γ-duals of the newly defined spaces. Further, we characterize some class of matrix mappings from the spaces M0q(Δqm) and Mcq(Δqm) to the spaces c,c0,cs,cs0,l∞,l1,bs. Lastly, compact operators are characterized on the spaces M0q(Δqm) using Hausdorff measure of noncompactness.