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Journal of Convex Analysis 29 (2022), No. 4, 1065--1082
Copyright Heldermann Verlag 2022

On the Convex Combination of Volterra Operators

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

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.

Keywords: Quadratic stochastic operator, Volterra operator, cubic stochastic operator.

MSC: 37N25; 92D10.

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