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

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 an...

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Main Authors: Hamzah, Nur Zatul Akmar, Karim, Siti Nurlaili, Selvarajoo, Mathuri, Sahabudin, Azida
格式: Article
语言:English
出版: Horizon Research Publishing 2022
主题:
QA Mathematics
在线阅读:http://irep.iium.edu.my/99273/2/99273_Dynamics%20of%20nonlinear%20operator%20generated.pdf
http://irep.iium.edu.my/99273/
https://www.hrpub.org/download/20220730/MS17-13427304.pdf
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spelling my.iium.irep.992732022-08-08T02:44:37Z http://irep.iium.edu.my/99273/ Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure Hamzah, Nur Zatul Akmar Karim, Siti Nurlaili Selvarajoo, Mathuri Sahabudin, Azida QA Mathematics 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. Horizon Research Publishing 2022 Article PeerReviewed application/pdf en http://irep.iium.edu.my/99273/2/99273_Dynamics%20of%20nonlinear%20operator%20generated.pdf 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 https://www.hrpub.org/download/20220730/MS17-13427304.pdf 10.13189/ms.2022.100417
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Hamzah, Nur Zatul Akmar
Karim, Siti Nurlaili
Selvarajoo, Mathuri
Sahabudin, Azida
Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure
description 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.
format Article
author Hamzah, Nur Zatul Akmar
Karim, Siti Nurlaili
Selvarajoo, Mathuri
Sahabudin, Azida
author_facet Hamzah, Nur Zatul Akmar
Karim, Siti Nurlaili
Selvarajoo, Mathuri
Sahabudin, Azida
author_sort Hamzah, Nur Zatul Akmar
title Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure
title_short Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure
title_full Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure
title_fullStr Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure
title_full_unstemmed Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure
title_sort dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure
publisher Horizon Research Publishing
publishDate 2022
url http://irep.iium.edu.my/99273/2/99273_Dynamics%20of%20nonlinear%20operator%20generated.pdf
http://irep.iium.edu.my/99273/
https://www.hrpub.org/download/20220730/MS17-13427304.pdf
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score 13.251813

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