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On a notion of rapidity of convergence used in the study of fixed point iterative methods. (English) Zbl 1389.40001
Summary: There exist many papers written in the last 50 years or so which are using a concept of rapidity of convergence for two comparable sequences. It appears that the original source of this notion is not known to most of the authors of those papers, since for this notion they refer to different sources or simply do not refer to any other publication, as though this notion woas “folklore” or even like they were the ones who introduced for the first time such a notion. Starting from this fact, the aim of the present note is to try to find out who was the true author of that notion of rapidity of convergence and, secondly, to illustrate how it is used in the particular case of the study of fixed point iterative methods.

MSC:
40A05 Convergence and divergence of series and sequences
47J25 Iterative procedures involving nonlinear operators
01A60 History of mathematics in the 20th century
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