Sul metodo delle approssimazioni successive: Convergenza globale e plus-convergenza globale
1988
With reference to the notions of global convergence and plus-global convergence introduced in [4], we prove that, for a dendriteX with a finite number of end points and a continuous mapF ofX into itself, the successive approximations method relative to pair (X, F) converges globally if and only ifF has no periodic points; furthermore, we show that ifF has no periodic points and the set of fixed points ofF is totally disconnected then the successive approximations method relative to the pair (X, F) plus-converge globally.
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