On homotopy of volterrian quadratic stochastic operators
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 operator...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Natural Publishing
2010
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/1559/ http://irep.iium.edu.my/1559/ http://irep.iium.edu.my/1559/1/mfsb-amis%282010%29.pdf |
| Summary: | 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, due to [3], 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 extension to the whole simplex. |
|---|