Abstract
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.
Original language | English |
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Pages (from-to) | 47-62 |
Number of pages | 16 |
Journal | Applied Mathematics and Information Sciences |
Volume | 4 |
Issue number | 1 |
Publication status | Published - 2010 |
Externally published | Yes |
Keywords
- Homotopy
- Tournaments
- Voterra quadratic stochastic operator
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics