U. A. Rozikov, U. U. Zhamilov, “$F$-Quadratic Stochastic Operators”, Mat. Zametki, 83:4 (2008), 606–612; Math. Notes, 83:4 (2008), 554

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Matematicheskie Zametki, 2008, Volume 83, Issue 4, Pages 606–612
DOI: https://doi.org/10.4213/mzm3778 (Mi mzm3778)

This article is cited in 55 scientific papers (total in 55 papers)

F

$F$ -Quadratic Stochastic Operators

U. A. Rozikov^a, U. U. Zhamilov^b

^a Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
^b Lycee no. 43

Full-text PDF (487 kB) Citations (55)

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DOI: https://doi.org/10.4213/mzm3778

Abstract: In this paper, we introduce the notion of an

F

$F$ ‑quadratic stochastic operator. It is shown that each

F

$F$ -quadratic operator has a unique fixed point. Besides, it is proved that any trajectory of an

F

$F$ -quadratic stochastic operator exponentially rapidly converges to this fixed point.

Keywords: quadratic stochastic operator, non-Volterra stochastic operator, ergodic theorem, mathematical genetics, fixed point of an operator.

Received: 28.02.2007
Revised: 10.04.2007

English version:
Mathematical Notes, 2008, Volume 83, Issue 4, Pages 554–559
DOI: https://doi.org/10.1134/S0001434608030280

Bibliographic databases:

UDC: 519.2

Language: Russian

Citation: U. A. Rozikov, U. U. Zhamilov, “

F

$F$ -Quadratic Stochastic Operators”, Mat. Zametki, 83:4 (2008), 606–612; Math. Notes, 83:4 (2008), 554–559

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm3778

https://doi.org/10.4213/mzm3778

https://www.mathnet.ru/eng/mzm/v83/i4/p606

This publication is cited in the following 55 articles:

U. U. Jamilov, Kh. O. Khudoyberdiev, “On the dynamics of non-Volterra quadratic operators corresponding to permutations”, Journal of Difference Equations and Applications, 30:3 (2024), 336
Abdessatar Souissi, Farrukh Mukhamedov, “Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains”, J Nonlinear Math Phys, 31:1 (2024)
Bobokhon Mamurov, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 040017
Uygun Jamilov, Farrukh Mukhamedov, Farzona Mukhamedova, Abdessatar Souissi, “Dynamics of nonlinear stochastic operators and associated Markov measures”, Math Methods in App Sciences, 2024
Uygun Jamilov, “Regular dynamics in a quadratic model”, Math Methods in App Sciences, 2024
B. Dzh. Mamurov, “Vypuklaya kombinatsiya dvukh kvadratichnykh stokhasticheskikh operatorov, deistvuyuschikh na $2D$ -simplekse”, Izv. vuzov. Matem., 2023, no. 7, 66–70
Uygun Jamilov, Farrukh Mukhamedov, Farzona Mukhamedova, “Discrete time model of sexual systems”, Heliyon, 9:7 (2023), e17913
B. J. Mamurov, “A Convex Combination of Two Quadratic Stochastic Operators Acting in the 2D Simplex”, Russ Math., 67:7 (2023), 55
F. F. Eshmatov, U. U. Jamilov, Kh. O. Khudoyberdiev, “Discrete time dynamics of a SIRD reinfection model”, Int. J. Biomath., 16:05 (2023)
A. Yu. Khamrayev, “Periodic and Regular Trajectories of Non-Volterra Quadratic Stochastic Operators”, Lobachevskii J Math, 44:10 (2023), 4321
Sh. B. Abdurakhimova, U. A. Rozikov, “Dynamical System of a Quadratic Stochastic Operator with Two Discontinuity Points”, Math. Notes, 111:5 (2022), 676–687
M. Saburov, Kh. Saburov, “Prilozheniya kvadratichnykh stokhasticheskikh operatorov k nelineinym problemam konsensusa”, Nauka — tekhnologiya — obrazovanie — matematika — meditsina, SMFN, 68, no. 1, Rossiiskii universitet druzhby narodov, M., 2022, 110–126
Uygun Jamilov, Kamola Aralova, Springer Proceedings in Mathematics & Statistics, 390, Infinite Dimensional Analysis, Quantum Probability and Applications, 2022, 357
I. T. Juraev, “Fixed Points of Quadratic Operators Defined on a Three-Dimensional Simplex of Idempotent Measures”, Lobachevskii J Math, 43:3 (2022), 762
Uygun U. Jamilov, Elbek Kh. Ziyodullaev, Springer Proceedings in Mathematics & Statistics, 390, Infinite Dimensional Analysis, Quantum Probability and Applications, 2022, 341
U. U. Jamilov, B. J. Mamurov, “Asymptotical Behavior of Trajectories of Non-Volterra Quadratic Stochastic Operators”, Lobachevskii J Math, 43:11 (2022), 3174
K. A. Aralova, U. U. Jamilov, “The dynamics of superposition of non-Volterra quadratic stochastic operators”, Journal of Difference Equations and Applications, 28:9 (2022), 1178
Jamilov U. Reinfelds A., “A Family of Volterra Cubic Stochastic Operators”, J. Convex Anal., 28:1 (2021), 19–30
Jamilov U. Ladra M., “Evolution Algebras and Dynamical Systems of a Worm Propagation Model”, Linear Multilinear Algebra, 2021
Jamilov U.U., Kurganov K.A., “On a Non-Volterra Cubic Stochastic Operator”, Lobachevskii J. Math., 42:12 (2021), 2800–2807

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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