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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.
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참고문헌 (32)
참고문헌 신청
M. Saburov / 2016 / Reaching a consensus: a discrete nonlinear time-varying case / Internat. J. Sys-tems Sci 47(10):2449~2457
T. A. Sarymsakov / 1990 / Analytic methods in the theory of quadratic stochastic processes / J. Theoret. Probab 3(1):51~70
S. Ulam / 1960 / A Collection of Mathematical Problems
M. Zakharevich / 1978 / On behavior of trajectories and the ergodic hypothesis for quadratic transformations of the simplex / Russian Math. Surveys 33(6):265~266
F. Mukhamedov / 2010 / On homotopy of volterrian quadratic stochastic op-erator / Appl. Math. Inf. Sci 4 (1) : 47 ~ 62
T. A. Sarymsakov / 1990 / Analytic methods in the theory of quadratic stochastic processes / J. Theoret. Probab 3(1):51~70
S. Ulam / 1960 / A Collection of Mathematical Problems
M. Zakharevich / 1978 / On behavior of trajectories and the ergodic hypothesis for quadratic transformations of the simplex / Russian Math. Surveys 33(6):265~266
F. Mukhamedov / 2010 / On homotopy of volterrian quadratic stochastic op-erator / Appl. Math. Inf. Sci 4 (1) : 47 ~ 62
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