Some Moduli of Angles in Banach Spaces

Abstract

In this paper, we mainly discuss the angle modulus of convexity δXa(ϵ) and the angle modulus of smoothness ρXa(ϵ) in a real normed linear space X, which are closely related to the classical modulus of convexity δX(ϵ) and the modulus of smoothness ρX(ϵ). Some geometric properties of the two moduli were investigated. In particular, we obtained a characterization of uniform non-squareness in terms of ρXa(1). Meanwhile, we studied the relationships between δXa(ϵ), ρXa(ϵ) and other geometric constants of real normed linear spaces through some equalities and inequalities. Moreover, these two coefficients were computed for some concrete spaces.