On the Convex Combination of Volterra Operators

Uygun Jamilov

Abstract

We consider a convex combination of certain Volterra operators defined on the two-dimensional simplex depending on the parameter θ, 0 ≤ θ ≤ 1, and study their trajectory behaviours. We divide the set of the parameter θ into two subsets such that on the first (resp. second) of them the corresponding Volterra operator is a regular (resp. non-ergodic) transformation.

Author information

Contact details are reproduced from the original publication and may be historical.

Uygun Jamilov

V. I. Romanovskiy Institute of Mathematics, and: Akfa University, and: National University of Uzbekistan, Tashkent, Uzbekistan

uygun.jamilov@mathinst.uz

Keywords

Quadratic stochastic operator
Volterra operator
cubic stochastic operator

Mathematics Subject Classification

37N25; 92D10

Suggested citation

U. Jamilov. “On the Convex Combination of Volterra Operators.” Journal of Convex Analysis 29 (2022), No. 4, 1065–1082.