Some Aspects of Geometric Constants in Modular Spaces

Abstract

In this paper, we generalize the typical geometric constants of Banach spaces to modular spaces. We study the equivalence between the convexity of modular and normed spaces, and obtain the relationship between ρ-Neumann-Jordan constant and ρ-James constant. In particular, we extend the convexity and smoothness modular, and obtain the criterion theorems of the uniform convexity and strict convexity.