Nasir Ganikhodjaev, Ramazon Muhitdinov, and M. Saburov P.O. Box 25200, Kuantan, Bukhara State University, P.O. Box 25200, Kuantan
Abstract : In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set $[0,1]$. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.
Keywords : Lebesgue nonlinear transformation, quadratic operator, measurable space