\(F\)-quadratic stochastic operators (Q2518008)

Motivated by applications to mathematical genetics, the authors study a special class of quad\-rat\-ic transformations of the unit simplex \(S^m\subset {\mathbb{R}}^{m+1}\) into itself. Using elementary methods, they prove that for each function from this class and any \(x^{(0)} \in S^m\) the trajectory \(\{ x^{(n)}\}\) is exponentially convergent to the fixed point \((1,0,...,0)\).