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On Homotopy of Volterrian Quadratic Stochastic Operators |
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PP: 47-62 |
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Author(s) |
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Farrukh Mukhamedov,
Mansoor Saburov,
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Abstract |
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| In the present paper we introduce a notion of homotopy of two Volterra operators which
is related to fixed points of such operators. We establish a criterion for determining
when two Volterra operators are homotopic, and as a consequence we obtain that the
corresponding tournaments of that operators are the same. This gives us a possibility
to know some information about the trajectory of homotopic Volterra operators. Moreover,
it is shown that any Volterra q.s.o. given on a face has at least two homotopic
extensions to the whole simplex. |
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