Normal Structure and Contractions which diminish Radius in Metric and Banach Spaces

TL;DR

This paper introduces fixed point results for orbitally contractions that reduce the radius of invariant convex sets in metric and Banach spaces, linking these results to the concept of weak normal structure.

Contribution

It provides new fixed point theorems for orbitally contractions that diminish the radius, and characterizes weak normal structure via fixed point properties.

Findings

Fixed point results for orbitally contractions with diminishing radius.

Characterization of weak normal structure through fixed point properties.

Extension of fixed point theory in metric and Banach spaces.

Abstract

In this paper, by using admissible sets, we give some fixed point results for orbitally contractions which diminish the radius of invariant convex subsets and orbits. Furthermore, a characterization of the weak normal structure by the fixed point property associated with this class of mappings is established.