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$F$-Quadratic Stochastic Operators

U. A. Rozikov^a, U. U. Zhamilov<sup>b

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

Abstract: In this paper, we introduce the notion of an $F$‑quadratic stochastic operator. It is shown that each $F$-quadratic operator has a unique fixed point. Besides, it is proved that any trajectory of an $F$-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.

UDC: 519.2

Received: 28.02.2007
Revised: 10.04.2007

DOI: 10.4213/mzm3778

 English version: Mathematical Notes, 2008, 83:4, 554–559

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