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Series-Like Iterative Functional Equation for PM Functions
(IOP Publishing Ltd, 2021) Suresh Kumar, M.; Murugan, V.
Given a non-empty subset X of the real line and a self map G on X, the functional equation representing G as an infinite linear combination of iterations of a self map g on X is known as the series-like functional equation. The solutions of the series-like functional equation have been studied only for the class of continuous strictly monotone functions. In this paper, we prove the existence of solutions of series-like functional equations for the class of continuous non-monotone functions using characteristic interval. Â© Published under licence by IOP Publishing Ltd.
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.