On surjective second order non-linear Markov operators and associated nonlinear integral equations

Mukhamedov, Farrukh and Khakimov, Otabek and Embong, Ahmad Fadillah (2018) On surjective second order non-linear Markov operators and associated nonlinear integral equations. Positivity. pp. 1-15. ISSN 1385-1292 E-ISSN 1572-9281 (In Press)

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Abstract

It was known that orthogonality preserving property and surjectivity of nonlinear Markov operators, acting on finite dimensional simpleces, are equivalent. It turns out that these notions are no longer equivalent when such kind of operators are considered over on infinite dimensional spaces. In the present paper, we find necessary and sufficient condition to be equivalent of these notions, for the second order nonlinear Markov operators. To do this, we fully describe all surjective second order nonlinear Markov operators acting on infinite dimensional simplex. As an application of this result, we provided some sufficient conditions for the existence of positive solutions of nonlinear integral equations whose domain are not compact.

Item Type:	Article (Journal)
Additional Information:	5537/65239
Uncontrolled Keywords:	Non-linear Markov operator, Quadratic stochastic operator, Orthogonality preserving, Surjective, Integral equation
Subjects:	Q Science > Q Science (General)
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	21 Aug 2018 10:14
Last Modified:	30 Jan 2019 11:12
URI:	http://irep.iium.edu.my/id/eprint/65239

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