Sul metodo delle approssimazioni successive: Convergenza globale e plus-convergenza globale

摘要

With reference to the notions of global convergence and plus-global convergence introduced in 4, we prove that, for a dendriteXwith a finite number of end points and a continuous mapFofXinto itself, the successive approximations method relative to pair (X, F) converges globally if and only ifFhas no periodic points; furthermore, we show that ifFhas no periodic points and the set of fixed points ofFis totally disconnected then the successive approximations method relative to the pair (X, F) plus-converge globally.