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Bull. Korean Math. Soc. 2017; 54(2): 607-618
Online first article January 31, 2017 Printed March 31, 2017
https://doi.org/10.4134/BKMS.b160212
Copyright © The Korean Mathematical Society.
On Lebesgue nonlinear transformations
Nasir Ganikhodjaev, Ramazon Muhitdinov, and M. Saburov
P.O. Box 25200, Kuantan, Bukhara State University, P.O. Box 25200, Kuantan
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
MSC numbers: 47HXX, 46TXX
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