On regularity of diagonally positive quadratic doubly stochastic operators

Saburov, Mansoor (2017) On regularity of diagonally positive quadratic doubly stochastic operators. Results in Mathematics, 72 (4). pp. 1907-1918. ISSN 1422-6383

	PDF - Published Version Restricted to Repository staff only Download (464kB) | Request a copy
Preview	PDF (SCOPUS) Download (189kB) | Preview

Abstract

The classical Perron–Frobenius theorem says that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix always converges to a unique fixed point. In general, an analogy of the Perron–Frobenius theorem does not hold for a quadratic stochastic operator associated with a positive cubic stochastic matrix. Namely, its trajectories may converge to different fixed points depending on initial points or may not converge at all. In this paper, we show regularity of quadratic doubly stochastic operators associated with diagonally positive cubic stochastic matrices. This is a nonlinear analogy of the Perron–Frobenius theorem for positive doubly stochastic matrices.

Item Type:	Article (Journal)
Additional Information:	6769/59920
Uncontrolled Keywords:	Quadratic doubly stochastic operator, cubic stochastic matrix, regularity.
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:	04 Dec 2017 11:42
Last Modified:	13 Mar 2018 16:24
URI:	http://irep.iium.edu.my/id/eprint/59920

Actions (login required)

View Item