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

TL;DR

This paper investigates the properties of three important moduli in metric fixed point theory within Banach spaces, examining their behavior, especially when they equal 1, and explores their dual space settings.

Contribution

It provides new insights into the properties of R(X), R(a, X), and RW(a, X), including their behavior in dual spaces and conditions when they equal 1.

Findings

Analysis of properties of R(X), R(a, X), RW(a, X)

Characterization of when these moduli equal 1

Extension of the study to dual space settings

Abstract

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.