On doubly stochastic quadratic operators and Birkhoff's problem
Rasul GanikhodzhaevDepartment of Mechanics and Mathematics ,, Na- tional University of Uzbekistan , Vuzgorodok , Tashkent , 100174 , UzbekistanFarruh ShahidiDepartment of Mechanics and Mathematics ,, National Uni- versity of Uzbekistan , Vuzgorodok , Tashkent , 100174 , Uzbekistan
2008en
ABI
Annotatsiya
In the present paper we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms convex polytope. Finally, we study analogue of Birkhoff's theorem for the class of doubly stochastic quadratic operators.
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