A study of paranormed sequence space defined by Motzkin matrix

The goal of this manuscript is to present the formulation of a novel regular matrix containing Motzkin numbers to obtain new paranormed sequence space \(\ell(\mathcal{M}, \mu, q)\) as the domain of Motzkin matrix on the space of absolutely \(p\)-summable sequences. Also, some topological properties and Schauder basis of the paranormed space \(\ell(\mathcal{M}, \mu, q)\) are introduced. Additionally, investigations have been made for computing their Kohe- Toeplitz dual, generalized Kothe-Toeplitz dual and Garling dual of the paranormed space \(\ell(\mathcal{M}, \mu, q)\). Finally, we emphasize on the characterization of certain matrix mappings from \(\ell(\mathcal{M}, \mu, q)\) into the classical sequence spaces.