On surjective second order non-linear Markov operators and associated nonlinear integral equations
| Autor: | Otabek Khakimov, Farrukh Mukhamedov, Ahmad Fadillah Embong |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Simplex Markov chain General Mathematics 010102 general mathematics 010103 numerical & computational mathematics Operator theory 01 natural sciences Domain (mathematical analysis) Potential theory Theoretical Computer Science Surjective function Nonlinear system Orthogonality 0101 mathematics Analysis Mathematics |
| Zdroj: | Positivity. 22:1445-1459 |
| ISSN: | 1572-9281 1385-1292 |
| DOI: | 10.1007/s11117-018-0587-0 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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