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Iterative roots of continuous functions with non-isolated forts
(Springer Science and Business Media B.V., 2020) Murugan, V.; Suresh Kumar, M.S.
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.
Iterative roots of PM functions extended from the characteristic interval
(Birkhauser, 2023) Murugan, V.; Suresh Kumar, M.S.; Jarczyk, J.; Jarczyk, W.
In this paper we consider the problem of finding iterative roots of order less than the number of forts of continuous piecewise monotone(PM) functions with nonmonotonicity height greater than one. We present sufficient conditions to extend iterative roots of PM functions from the characteristic interval which determines the behavior of the function under iteration. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.