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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| Format: | Article |
| Language: | English English |
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Horizon Research Publishing
2022
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| Online Access: | http://umpir.ump.edu.my/id/eprint/40127/1/Dynamics%20of%20nonlinear%20operator%20generated%20by%20lebesgue%20quadratic.pdf http://umpir.ump.edu.my/id/eprint/40127/2/Dynamics%20of%20nonlinear%20operator%20generated%20by%20lebesgue%20quadratic_ABS.pdf |
| _version_ | 1825815425953300480 |
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| author | Nur Zatul Akmar, Hamzah Siti Nurlaili, Karim Selvarajoo, Mathuri Noor Azida, Sahabudin |
| author_facet | Nur Zatul Akmar, Hamzah Siti Nurlaili, Karim Selvarajoo, Mathuri Noor Azida, Sahabudin |
| author_sort | Nur Zatul Akmar, Hamzah |
| collection | UMP |
| 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 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. |
| first_indexed | 2024-03-06T13:13:17Z |
| format | Article |
| id | UMPir40127 |
| institution | Universiti Malaysia Pahang |
| language | English English |
| last_indexed | 2024-03-06T13:13:17Z |
| publishDate | 2022 |
| publisher | Horizon Research Publishing |
| record_format | dspace |
| spelling | UMPir401272024-02-05T03:19:15Z http://umpir.ump.edu.my/id/eprint/40127/ Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure Nur Zatul Akmar, Hamzah Siti Nurlaili, Karim Selvarajoo, Mathuri Noor Azida, Sahabudin QA75 Electronic computers. Computer science QA76 Computer software T Technology (General) TA Engineering (General). Civil engineering (General) 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. Horizon Research Publishing 2022-07 Article PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/40127/1/Dynamics%20of%20nonlinear%20operator%20generated%20by%20lebesgue%20quadratic.pdf pdf en http://umpir.ump.edu.my/id/eprint/40127/2/Dynamics%20of%20nonlinear%20operator%20generated%20by%20lebesgue%20quadratic_ABS.pdf Nur Zatul Akmar, Hamzah and Siti Nurlaili, Karim and Selvarajoo, Mathuri and Noor Azida, Sahabudin (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. (Published) https://doi.org/10.13189/ms.2022.100417 https://doi.org/10.13189/ms.2022.100417 |
| spellingShingle | QA75 Electronic computers. Computer science QA76 Computer software T Technology (General) TA Engineering (General). Civil engineering (General) Nur Zatul Akmar, Hamzah Siti Nurlaili, Karim Selvarajoo, Mathuri Noor Azida, Sahabudin Dynamics of nonlinear operator generated by lebesgue quadratic stochastic operator with exponential measure |
| title | 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_short | 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 |
| topic | QA75 Electronic computers. Computer science QA76 Computer software T Technology (General) TA Engineering (General). Civil engineering (General) |
| url | http://umpir.ump.edu.my/id/eprint/40127/1/Dynamics%20of%20nonlinear%20operator%20generated%20by%20lebesgue%20quadratic.pdf http://umpir.ump.edu.my/id/eprint/40127/2/Dynamics%20of%20nonlinear%20operator%20generated%20by%20lebesgue%20quadratic_ABS.pdf |
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