Faculty Publications
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Item Iterative Roots of Non-PM Functions and Denseness(Birkhauser Verlag AG, 2018) Cho, Y.J.; Suresh Kumar, S.K.; Murugan, M.The characteristic interval plays a vital role on the existence of iterative roots of PM functions with height less than or equal to one. In this paper, we define the characteristic interval for continuous functions and prove theorems on extension and nonexistence of iterative roots for a class of continuous non-PM functions on a closed and bounded interval I. Also, we prove that a class of continuous non-PM functions, which do not possess any iterative roots, is dense in C(I, I). © 2018, Springer International Publishing AG, part of Springer Nature.Item Dynamics of the iteration operator on the space of continuous self-maps(American Mathematical Society, 2021) Murugan, M.; Gopalakrishna, C.; Zhang, W.The semi-dynamical system of a continuous self-map is generated by iteration of the map, however, the iteration itself, being an operator on the space of continuous self-maps, may generate interesting dynamical behaviors. In this paper we prove that the iteration operator is continuous on the space of all continuous self-maps of a compact metric space and therefore induces a semi-dynamical system on the space. Furthermore, we characterize its fixed points and periodic points in the case that the compact metric space is a compact interval by discussing the Babbage equation. We prove that all orbits of the iteration operator are bounded but most fixed points are not stable. On the other hand, we prove that the iteration operator is not chaotic. © 2020 American Mathematical Society.Item Convergence analysis of a class of iterative methods: a unified approach(Vilnius Gediminas Technical University, 2025) Murugan, M.; Godavarma, C.; George, S.; Bate, I.; Senapati, K.In this paper, we study the convergence of a class of iterative methods for solving the system of nonlinear Banach space valued equations. We provide a unified local and semi-local convergence analysis for these methods. The convergence order of these methods are obtained using the conditions on the derivatives of the involved operator up to order 2 only. Further, we provide the number of iterations required to obtain the given accuracy of the solution. Various numerical examples including integral equations and Caputo fractional differential equations are considered to show the performance of our methods. © 2025 The Author(s). Published by Vilnius Gediminas Technical University.