An Overview of Generalized Cesàro Sequence Spaces in Geometric Calculus

Abstract

In this study, we introduce the generalized Cesàro sequence space in geometric calculus and establish a G-modular on this space. The generalized geometric Cesàro sequence space is equipped with the Luxemburg G-norm induced by the G-modular. The connections of the G-modular and Luxemburg G-norm on this space are studied. In addition, we show that the generalized geometric Cesàro sequence space is a G-Banach space under the Luxemburg G-norm and it is G-nonsquare where pn > 1 for all n ∈ ℕ.