Iterative roots of exclusive multifunctions

TL;DR

This paper studies iterative roots of a special class of monotone upper semi-continuous multifunctions with finitely many jumps, introducing the concept of intensity and constructing roots for exclusive multifunctions with an absorbing interval.

Contribution

It introduces the concept of intensity to analyze jump growth and constructs iterative roots for exclusive multifunctions with an absorbing interval.

Findings

Identifies a class of exclusive multifunctions with intensity 1.

Establishes the existence of iterative roots for these exclusive multifunctions.

Provides a method to construct roots of any order for the class.

Abstract

In this paper we investigate iterative roots of strictly monotone upper semi-continuous multifunctions having finitely many jumps. Known results are concerning roots of order 2 for multifunctions of exact one jump. For the general investigation, we introduce a concept `intensity' to formulate the growth of jumps under iteration and find a class of strictly monotone and upper semi-continuous multifunctions of intensity 1, called exclusive multifunctions, each of which has an absorbing interval. Then we use the absorbing interval to construct iterative roots of order $n$ for those exclusive multifunctions.