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Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure

Hamzah, Nur Zatul Akmar and Karim, Siti Nurlaili and Selvarajoo, Mathuri and Sahabudin, Azida (2022) Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure. Mathematics and Statistics, 10 (4). pp. 861-867. ISSN 2332-2071 E-ISSN 2332-2144

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Quadratic stochastic operator (QSO) is a branch of nonlinear operator studies initiated by Bernstein in 1924 through his presentation on population genetics. The study of QSO is still ongoing due to the incomplete understanding of the trajectory behavior of such operators given certain conditions and measures. In this paper, we intend to introduce and investigate a class of QSO named Lebesgue QSO which gets its name from the Lebesgue measure as the measure is used to define the probability measure of such QSO. The broad definition of Lebesgue QSO allows the construction of a new measure as its family of probability measure. We construct a class of Lebesgue QSO with exponential measure generated by 3-partition with three different parameters defined on continual state space. Also, we present the dynamics of such QSO by describing the fixed points and periodic points of the system of equations generated by the defined QSO using a functional analysis approach. The investigation is concluded by the regularity of the operator, where such Lebesgue QSO is either regular or nonregular depending on the parameters and defined measurable partitions. The result of this research allows us to define a new family of functions of the probability measure of Lebesgue QSO and compare their dynamics with the existing Lebesgue QSO.

Item Type: Article (Journal)
Uncontrolled Keywords: Quadratic Stochastic Operator, Lebesgue Measure, Regularity, Partition, Periodic Points
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Kulliyyah of Science
Depositing User: Nur Zatul Akmar Hamzah
Date Deposited: 08 Aug 2022 10:42
Last Modified: 08 Aug 2022 10:44
URI: http://irep.iium.edu.my/id/eprint/99273

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