Properties of $R(X), R(a, X) \mbox{ and } RW(a, X)$

In the context of metric fixed point theory in Banach spaces three moduli have played an important role. These are R(X), R(a, X) and RW(a, X). This paper looks at some of their properties. Also investigated is what happens when they take on the value of 1. The situation where these moduli are set in dual space is also considered.