A new moduli for Banach spaces, Dunkl-Williams constant and Holder continuity of radial projection
A new moduli for Banach spaces, Dunkl-Williams constant and Holder continuity of radial projection
Abstract Let $X$ be a Banach space and let $DW(X)$ denotes the Dunkl-Williams constant of $X$. In this paper, we first introduce moduli $ \gamma_{X}:[0,2] \to [0,1]$ and show that $DW(X)=\sup\limits_{0<\epsilon \leq 2}\frac{\epsilon}{\gamma_{X}(\epsilon)}$, which provides a simple formula for calculating $DW(X)$ in terms of $\gamma_{X}(\epsilon)$. Then, we compute $\gamma_{H}(\epsilon)$, where …