Iterative roots of continuous functions with non-isolated forts

Abstract

Iterative root problem is one of the classical problem in analysis and isdescribed as follows: given a topological space X, a continuous self map F on X and a fixed positive integer n, to find another self map f on X such that fn= F. This problem is solved only for a particular class of continuous functions and is still unsolved for any continuous function. In this paper, we present results on non-existence of iterative roots of continuous functions having finitely manynon-isolated forts. © 2017, Forum D'Analystes, Chennai.