Geodesic
$F$-Quadratic Stochastic Operators
Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 606-612

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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. 
@article{MZM_2008_83_4_a11,
     author = {U. A. Rozikov and U. U. Zhamilov},
     title = {$F${-Quadratic} {Stochastic} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {606--612},
     publisher = {mathdoc},
     volume = {83},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a11/}
}
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U. A. Rozikov; U. U. Zhamilov. $F$-Quadratic Stochastic Operators. Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 606-612. http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a11/