On homotopy of volterrian quadratic stochastic operators

Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

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 languageEnglish
Pages (from-to)47-62
Number of pages16
JournalApplied Mathematics and Information Sciences
Volume4
Issue number1
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • Homotopy
  • Tournaments
  • Voterra quadratic stochastic operator

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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