On Berinde's method for comparing iterative processes
Abstract
In the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in [Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2004, no. 2, 97--105] because it seems to be very successful. In fact, if IP1 and IP2 are two iterative processes converging to the same element, then IP1 is faster than IP2 in the sense of Berinde. The aim of this note is to prove this almost obvious assertion and to discuss briefly several papers that cite the mentioned Berinde's paper and use his method for comparing iterative processes.
Cite
@article{arxiv.1812.00958,
title = {On Berinde's method for comparing iterative processes},
author = {C. Zalinescu},
journal= {arXiv preprint arXiv:1812.00958},
year = {2025}
}
Comments
27 pages; beside adding more than 100 references published mainly after 2020, one comments the use of Berinde's method in the proof of the main result from Berinde's 2004 paper, as well as a remark of Ali and Ali (2020) paper concerning Popescu's method and the proof of his main result