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primary topic: Dynamics of Nonlinear Operator Generated by Lebesgue Quadratic Stochastic Operator with Exponential Measure

Dynamics of Nonlinear Operator Generated by Lebesgue Quadratic Stochastic Operator with Exponential Measure
type: AcademicArticle
type: Article
abstract: 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 X = 0,1 . 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. © 2022 by authors, all rights reserved.
date: 2022
volume: 10
issue: 4
is part of: Mathematics and Statistics
status: peerReviewed
status: published
author list: authors
type: EPrint
type: ArticleEPrint
is part of: repository

Horizon Research Publishing
type: Organization

Mathematics and Statistics
type: Collection
issn: 23322071

Mathuri Selvarajoo
type: Person
given name: Mathuri
family name: Selvarajoo

Nur Zatul Akmar Hamzah
type: Person
given name: Nur Zatul Akmar
family name: Hamzah

Siti Nurlaili Karim
type: Person
given name: Siti Nurlaili
family name: Karim

Noor Azida Sahabudin
type: Person
given name: Noor Azida
family name: Sahabudin

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primary topic: Dynamics of Nonlinear Operator Generated by Lebesgue Quadratic Stochastic Operator with Exponential Measure