Faculty Publications
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Item NON-ISOLATED, NON-STRICTLY MONOTONE POINTS OF ITERATES OF CONTINUOUS FUNCTIONS(Michigan State University Press, 2021) Murugan, V.; Palanivel, R.There are continuous functions with complicated yet interesting sets of non-isolated non-strictly monotone points. This paper aims to characterize the sets of isolated and non-isolated non-strictly monotone points of the composition of continuous functions. Consequently, an uncountable dense set of measure zero in the real line and whose complement is also uncountable and dense is obtained. © 2021 Michigan State University Press. All rights reserved.Item Iterative roots of continuous functions and Hyers–Ulam stability(Birkhauser, 2021) Murugan, V.; Palanivel, R.In this paper, we prove that continuous non-PM functions with non-monotonicity height equal to 1 need not be strictly monotone on its range, unlike PM functions. An existence theorem is obtained for the iterative roots of such functions. We also discuss the Hyers–Ulam stability for the functional equation of the iterative root problem. © 2020, Springer Nature Switzerland AG.Item Hyers-Ulam stability of an iterative equation for strictly increasing continuous functions(Birkhauser, 2023) Palanivel, R.; Murugan, V.The Hyers-Ulam stability of the iterative equation fn= F for continuous functions F was studied under the assumptions that F is a homeomorphism on its range, and the equation has stability on its range. It is important to study the stability of the equation for homeomorphisms on intervals. In this paper, theorems on stability are obtained using the properties of monotonic approximate solutions. The method is based on the stability of two derived iterative equations. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.