On infinite dimensional quadratic Volterra operators

Farruh Mukhamedov, Hasan Akin, Seyit Temir

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In addition, it is described its extreme points. Besides, we study certain limit behaviors of such operators and give some more examples of Volterra operators for which their trajectories do not converge. Finally, we define a compatible sequence of finite dimensional Volterra operators and prove that any power of this sequence converges in weak topology.

Original languageEnglish
Pages (from-to)533-556
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Volume310
Issue number2
DOIs
Publication statusPublished - Oct 15 2005
Externally publishedYes

Keywords

  • Compatibility
  • Infinite dimensional space
  • Quadratic stochastic operator
  • Volterra operator
  • Weak compact

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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