A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the s...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 14; no. 1; p. 123
Main Author: Berinde, Vasile
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2022
Subjects:
Algorithms
Approximation
Convergence
Enrichment
Hilbert space
Iterative algorithms
Iterative methods
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the simple Krasnosel’skiǐ fixed point algorithm. Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel’skiǐ fixed point algorithm than with the modified Krasnosel’skiǐ–Mann algorithm.
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content type line 14
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14010123