Characterization of Non-Isolated Forts and Stability of an Iterative Functional Equation

dc.contributor.advisorMurugan, V.
dc.contributor.authorPalanivel, R.
dc.date.accessioned2022-02-01T10:58:18Z
dc.date.available2022-02-01T10:58:18Z
dc.date.issued2021
dc.description.abstractThe problem of finding a solution f : X →X of the iterative functional equation f n = F for a given positive integer n ≥ 2 and a function F : X → X on a non-empty set X is known as the iterative root problem. The non-strictly monotone points (or forts) of F play an essential role in finding a continuous solution f of f n = F whenever X is an interval in the real line. In this thesis, we define the forts for any continuous function f : I →J, where I and J are arbitrary intervals in the real line R. We study the non-monotone behavior of forts under composition and characterize the sets of isolated and non-isolated forts of iterates of any continuous self-map on an arbitrary interval I to study the continuous solutions of f n = F. Consequently, we obtain an example of an uncountable measure zero dense set of non-isolated forts in the real line. We define the notions of iteratively closed set in the space of continuous self-maps and the non-monotonicity height of any continuous self-map. We prove that continuous self-maps of non-monotonicity height 1 need not be strictly monotone on its range, unlike continuous piecewise monotone functions. Also, we obtain sufficient conditions for the existence of continuous solutions of f n = F for a class of continuous functions of non-monotonicity height 1. Further, we discuss the Hyers-Ulam stability of the iterative functional equation f n = F for continuous self-maps of non-monotonicity height 0 and 1.en_US
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/17073
dc.language.isoenen_US
dc.publisherNational Institute of Technology Karnataka, Surathkalen_US
dc.subjectDepartment of Mathematical and Computational Sciencesen_US
dc.subjectFunctional equationsen_US
dc.subjectIterative rootsen_US
dc.subjectNon-isolated fortsen_US
dc.subjectCantor seten_US
dc.subjectMeasure zero dense seten_US
dc.subjectIteratively closed seten_US
dc.subjectNon-monotonicity heighten_US
dc.subjectCharacteristic intervalen_US
dc.subjectNon-PM functionsen_US
dc.subjectHyers-Ulam stabilityen_US
dc.titleCharacterization of Non-Isolated Forts and Stability of an Iterative Functional Equationen_US
dc.typeThesisen_US

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