eprintid: 20310
rev_number: 3
eprint_status: archive
userid: 1
dir: disk0/00/02/03/10
datestamp: 2025-11-03 08:49:34
lastmod: 2025-11-03 08:49:34
status_changed: 2025-11-03 08:49:34
type: article
metadata_visibility: show
creators_name: Hamzah, Nur Zatul Akmar
creators_name: Karim, Siti Nurlaili
title: ON LEBESGUE QUADRATIC STOCHASTIC OPERATORS WITH EXPONENTIAL MEASURE GENERATED BY 3-PARTITION
ispublished: pub
note: Cited by: 0; All Open Access, Bronze Open Access
abstract: 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 QSO study defined on such a state space, we consider a QSO class on continuous state space in this work. It is known as Lebesgue QSO, which is an exponential measure generated by three measurable partitions with three parameters. We specify two distinct cases of three parameters, which are represented by reducible QSOs. We demonstrate that such a reducible QSO can be reduced to a one-dimensional simplex. Consequently, we analyse the dynamics of such operators by employing the first derivative 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 second-order cycle. Corresponding to a strong limit of the sequence of the reduced QSO, such an operator is regular. Meanwhile, such an operator is a nonregular transformation when a second-order cycle exists. © UMT Press
date: 2025
publisher: Universiti Malaysia Terengganu
official_url: https://www.scopus.com/inward/record.uri?eid=2-s2.0-105007313879&doi=10.46754%2fjssm.2025.05.005&partnerID=40&md5=4b6e33ffe31252124fe8f396c4ce3b43
id_number: 10.46754/jssm.2025.05.005
full_text_status: none
publication: Journal of Sustainability Science and Management
volume: 20
number: 5
pagerange: 963 – 975
refereed: TRUE
issn: 18238556
citation:   Hamzah, Nur Zatul Akmar and Karim, Siti Nurlaili  (2025) ON LEBESGUE QUADRATIC STOCHASTIC OPERATORS WITH EXPONENTIAL MEASURE GENERATED BY 3-PARTITION.  Journal of Sustainability Science and Management, 20 (5).  963 – 975.  ISSN 18238556