Sequence spaces derived by \(q_{\lambda}\) operators in \(\ell _{p}\) spaces and their geometric properties

In this paper, we establish a novel category of sequence spaces ${\ell }_p^{q_{\lambda }}$ $\ell _{p}^{q_{\lambda}}$ and ${\ell }_{\mathrm{\infty }}^{q_{\lambda }}$ $\ell _{\infty}^{q_{\lambda}}$ by utlizing q-analogue ${\mathrm{\Lambda }}^q$ $\Lambda^{q}$ of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ${\ell }_p$ $\ell _{p}$ and ${\ell }_{\mathrm{\infty }}$ $\ell _{\infty}$ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class $({\ell }_p^{q_{\lambda }},X)$ $(\ell _{p}^{q_{\lambda}},X)$ of matrices, where X is any of the spaces ${\ell }_{\mathrm{\infty }}$ $\ell _{\infty }$ , c, or $c_0$ $c_{0}$ . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ${\ell }_p^{q_{\lambda }}$ $\ell _{p}^{q_{\lambda}}$ .