On non-linear Markov operators: surjectivity vs orthogonal preserving property |
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Authors: | Farrukh Mukhamedov Ahmad Fadillah Embong |
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Affiliation: | 1. Department of Mathematical Sciences, College of Science, The United Arab Emirates University , Al Ain, UAE.;2. Department of Computational &3. Theoretical Sciences, Faculty of Science, International Islamic University Malaysia , Kuantan, Malaysia. |
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Abstract: | In the present paper, we consider non-linear Markov operators, namely polynomial stochastic operators. We introduce a notion of orthogonal preserving polynomial stochastic operators. The purpose of this study is to show that surjectivity of non-linear Markov operators is equivalent to their orthogonal preserving property. |
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Keywords: | Polynomial stochastic operator surjective orthogonal preserving |
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