Regularity of Geometric quadratic stochastic operator generated by 2-partition of infinite points
Siti Nurlaili KarimDepartment of Computational and Theoretical Sciences,
Kulliyyah of Science,
International Islamic University Malaysia,
Jalan Sultan Ahmad Shah,
Bandar Indera Mahkota,
25200 Kuantan, Pahang, MalaysiaNur Zatul Akmar HamzahDepartment of Computational and Theoretical Sciences,
Kulliyyah of Science,
International Islamic University Malaysia,
Jalan Sultan Ahmad Shah,
Bandar Indera Mahkota,
25200 Kuantan, Pahang, MalaysiaNasir GanikhodjaevDepartment of Computational and Theoretical Sciences,
Kulliyyah of Science,
International Islamic University Malaysia,
Jalan Sultan Ahmad Shah,
Bandar Indera Mahkota,
25200 Kuantan, Pahang, Malaysia
2020en
ABI
Abstract
In this research, we construct a class of quadratic stochastic operator called Geometric quadratic stochastic operator generated by arbitrary 2-partition of infinite points on a countable state space , where . We also study the limiting behavior of such operator by proving the existence of the limit of the sequence through the convergence of the trajectory to a unique fixed point. It is established that such operator is a regular transformation.
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Cited by 20 references