On divergence of any order cesaaro mean of lotka-volterra operators

Saburov, Mansoor (2015) On divergence of any order cesaaro mean of lotka-volterra operators. Annals of Functional Analysis, 6 (4). pp. 247-254. ISSN 2008-8752 (O)

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Abstract

Based on some numerical calculations, S.M. Ulam has conjectured that the ergodic theorem holds true for any quadratic stochastic operator acting on the finite dimensional simplex. However, M.I. Zakharevich showed that Ulam's conjecture is false in general. Later, N.N. Ganikhodjaev and D.V. Zanin have generalized Zakharevich's example in the class of quadratic stochastic Volterra operators acting on 2D simplex. In this paper, we provide a class of Lotka-Volterra operators for which any order Cesáaro mean diverges. This class of Lotka-Volterra operators encompasses all previously presented operators in this context.

Item Type:	Article (Journal)
Additional Information:	6769/45053
Uncontrolled Keywords:	Cesáaro mean; Ergodic theorem; Lotka-Volterra operator
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr Mansoor Saburov
Date Deposited:	12 Oct 2015 09:12
Last Modified:	16 Aug 2017 16:28
URI:	http://irep.iium.edu.my/id/eprint/45053

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