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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.
Subcommuting and comparable iterative roots of order preserving homeomorphisms
(Emerald Group Holdings Ltd., 2019) Murugan, V.; Suresh Kumar, M.
It is known that the iterative roots of continuous functions are not necessarily unique, if it exist. In this note, by introducing the set of points of coincidence, we study the iterative roots of order preserving homeomorphisms. In particular, we prove a characterization of identical iterative roots of an order preserving homeomorphism using the points of coincidence of functions. © 2019, Veerapazham Murugan and Murugan Suresh Kumar.