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On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition

Quadratic stochastic operator (QSO) is a continuously expanding topic in nonlinear operator theory due to its immense applications in various disciplines. Inspired by the notion of infinite state space as there is limited literature on the study of QSO defined on such state space, in this paper, we...

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Main Authors: Karim, Siti Nurlaili, Hamzah, Nur Zatul Akmar
Format: Conference or Workshop Item
Language:English
Published: Department of Computational and Theoretical Sciences, Kulliyyah of Science, IIUM 2023
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/106848/7/106848_On%20Lebesgue%20Quadratic%20Stochastic%20Operators.pdf
http://irep.iium.edu.my/106848/
https://conference.iium.edu.my/icmcts/2023/index.php/downloads/
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spelling my.iium.irep.1068482023-09-20T05:02:08Z http://irep.iium.edu.my/106848/ On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition Karim, Siti Nurlaili Hamzah, Nur Zatul Akmar QA Mathematics Quadratic stochastic operator (QSO) is a continuously expanding topic in nonlinear operator theory due to its immense applications in various disciplines. Inspired by the notion of infinite state space as there is limited literature on the study of QSO defined on such state space, in this paper, we consider a class of QSO on continuous state space, called Lebesgue QSO with exponential measure generated by three measurable partitions with three parameters. We define two different cases of three parameters which represent by a reducible QSO. We demonstrate that such a reducible QSO can be reduced to a one-dimensional setting. Then, we analyze the dynamics of such operators by employing the Jacobian matrix method and show that the operators may have either an attracting fixed point to indicate the existence of a strong limit or a non-attracting fixed point to suggest the presence of a cycle of second-order. Corresponding to the existence of a strong limit of the sequence of the reduced QSO, such operator is a regular transformation. Meanwhile, such operator is a nonregular transformation when a second-order cycle exists. Department of Computational and Theoretical Sciences, Kulliyyah of Science, IIUM 2023-08-10 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/106848/7/106848_On%20Lebesgue%20Quadratic%20Stochastic%20Operators.pdf Karim, Siti Nurlaili and Hamzah, Nur Zatul Akmar (2023) On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition. In: INTERNATIONAL CONFERENCE ON MATHEMATICS: COMPUTATIONAL AND THEORETICAL SCIENCES, 8-10 August 2023, Swiss-Belhotel Kuantan, Pahang. (Unpublished) https://conference.iium.edu.my/icmcts/2023/index.php/downloads/
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
Karim, Siti Nurlaili
Hamzah, Nur Zatul Akmar
On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition
description Quadratic stochastic operator (QSO) is a continuously expanding topic in nonlinear operator theory due to its immense applications in various disciplines. Inspired by the notion of infinite state space as there is limited literature on the study of QSO defined on such state space, in this paper, we consider a class of QSO on continuous state space, called Lebesgue QSO with exponential measure generated by three measurable partitions with three parameters. We define two different cases of three parameters which represent by a reducible QSO. We demonstrate that such a reducible QSO can be reduced to a one-dimensional setting. Then, we analyze the dynamics of such operators by employing the Jacobian matrix method and show that the operators may have either an attracting fixed point to indicate the existence of a strong limit or a non-attracting fixed point to suggest the presence of a cycle of second-order. Corresponding to the existence of a strong limit of the sequence of the reduced QSO, such operator is a regular transformation. Meanwhile, such operator is a nonregular transformation when a second-order cycle exists.
format Conference or Workshop Item
author Karim, Siti Nurlaili
Hamzah, Nur Zatul Akmar
author_facet Karim, Siti Nurlaili
Hamzah, Nur Zatul Akmar
author_sort Karim, Siti Nurlaili
title On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition
title_short On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition
title_full On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition
title_fullStr On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition
title_full_unstemmed On Lebesgue Quadratic Stochastic Operators with exponential measure generated by 3-partition
title_sort on lebesgue quadratic stochastic operators with exponential measure generated by 3-partition
publisher Department of Computational and Theoretical Sciences, Kulliyyah of Science, IIUM
publishDate 2023
url http://irep.iium.edu.my/106848/7/106848_On%20Lebesgue%20Quadratic%20Stochastic%20Operators.pdf
http://irep.iium.edu.my/106848/
https://conference.iium.edu.my/icmcts/2023/index.php/downloads/
_version_ 1778160497696178176
score 13.2442

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