Fixed points of continuous rotative mappings on the real line

TL;DR

This paper proves that every continuous rotative mapping on a closed interval in the real line has at least one fixed point, resolving some open questions in the field.

Contribution

It establishes the existence of fixed points for continuous rotative mappings on closed intervals, providing new insights into their behavior.

Findings

Every continuous rotative mapping on a closed interval has a fixed point.

The result answers previously open questions by Goebel and Koter.

The proof applies to all such mappings on the real line.

Abstract

We show that every continuous rotative mapping on a closed interval has a fixed point. This gives an answer to some open questions raised by Goebel and Koter.