Abstract

We consider a convex combination of non-Volterra quadratic stochastic operators defined on the two-dimensional simplex depending on a parameter λ and study their trajectory behaviours. We show that for any λ∈[0, 1] and for any initial point the set of limit points of the trajectory is a singleton. We also prove that a superposition of these non-Volterra quadratic stochastic operators is a regular transformation.

Author information

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

Uygun U. Jamilov

(1) V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
(2) National University of Uzbekistan, Tashkent, Uzbekistan
and: New Uzbekistan University, Tashkent, Uzbekistan

uygun.jamilov@mathinst.uz

Keywords

  • Quadratic stochastic operator
  • Volterra and non-Volterra operator
  • trajectory

Mathematics Subject Classification

37N25, 92D10

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Suggested citation

U. U. Jamilov, R. T. Mukhitdinov. “Dynamics of a Convex Combination and Superposition of Non-Volterra Quadratic Stochastic Operators.” Journal of Convex Analysis 32 (2025), No. 4, 975–988. https://doi.org/10.68381/jca32052

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press LLC.