q-Cesàro double sequence space ℒ˜sq$$\tilde {\cal L}_s^q$$ derived by q-analog

Abstract

Abstract This study includes the new Banach space ℒ˜sq$$\tilde {\cal L}_s^q$$ designed as the domain in 𝓛s space of the 4d (4-dimensional) q-Cesàro matrix obtained as the q-analog of the well-known 4d Cesàro matrix. After showing the completeness of the aforementioned space, giving some inclusion relations, determining the fundamental set of this space and calculating the duals, finally, some matrix transformations related to the new space were characterized.