Mukhamedov, F. and Khakimov, O. and Embong, A. F. (2021) Projective surjectivity of quadratic stochastic operators on L1 and its application. Chaos, Solitons and Fractals, 148 (NA). p. 111034. ISSN 09600779

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Official URL: http://dx.doi.org/10.1016/j.chaos.2021.111034
Abstract
A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over an infinite state space can be identified by a continuous mapping (the socalled nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex). In the present paper, we consider a continuous analogue of the mentioned mapping acting on L1spaces. Main aim of the current paper is to investigate projective surjectivity of quadratic stochastic operators (QSO) acting on the set of all probability measures. To prove the main result, we study the surjectivity of infinite dimensional nonlinear Markov operators and apply them to the projective surjectivity of the considered QSO. Furthermore, the obtained results are applied to the existence of the positive solution of some Hammerstein integral equations.
Item Type:  Article 

Uncontrolled Keywords:  nonlinear equation, projective surjection, quadratic stochastic operator 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  96514 
Deposited By:  Narimah Nawil 
Deposited On:  26 Jul 2022 08:03 
Last Modified:  26 Jul 2022 08:03 
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