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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 4 > No. 1


On Homotopy of Volterrian Quadratic Stochastic Operators

PP: 47-62
Farrukh Mukhamedov, Mansoor Saburov,
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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