A new perspective on paranormed Riesz sequence space of non-absolute type

The current article mainly dwells on introducing Riesz sequence space \(r^{q}(\widetilde{B}_{u}^{p})\) which generalized the prior studies of Candan and Güneş [28], Candan and Kılınç [30]  and consists of all sequences whose \(R_{u}^{q}\widetilde{B}\)-transforms are in the space \(\ell(p)\), where \(\widetilde{B}=B(r_{n},s_{n})\) stands for double sequential band matrix \((r_{n})^{\infty}_{n=0}\) and \((s_{n})^{\infty}_{n=0}\) are given convergent sequences of positive real numbers. Some topological properties of the new brand sequence space have been investigated as well as \(\alpha\)- \(\beta\)-and \(\gamma\)-duals. Additionally, we have also constructed the basis of \(r^{q}(\widetilde{B}_{u}^{p})\). Eventually, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.