On Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators

This paper observes that a definition adopted by some authors for comparing the rates of convergence of two iteration schemes is not correct. The paper further proves that the Picard iteration scheme converges faster than the Mann iteration scheme for contraction mappings and quasi-contraction mappings satisfying Zamfirescu conditions, in an arbitrary Banach space.

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Publication Details

Journal
Annals of Mathematics and Computer Science
Published
2025-03-23
DOI
https://doi.org/10.56947/amcs.v27.454
Primary Topic
Matrix Theory and Algorithms
Type
article
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article

On Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators

Aniefiok Udomene
Annals of Mathematics and Computer Science
Matrix Theory and Algorithms
article

On Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators

Aniefiok Udomene
article en

Abstract

This paper observes that a definition adopted by some authors for comparing the rates of convergence of two iteration schemes is not correct. The paper further proves that the Picard iteration scheme converges faster than the Mann iteration scheme for contraction mappings and quasi-contraction mappings satisfying Zamfirescu conditions, in an arbitrary Banach space.

Annals of Mathematics and Computer ScienceVol. 27
Michael Okpara University of Agriculture (NG)
Openalex Percentile: Top 94%
Matrix Theory and Algorithms
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On Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators — Aniefiok Udomene · Annals of Mathematics and Computer Science (2025) | TGRS Research Map | TGRS