<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The purpose of this note is to discuss the recent paper of Espínola and Wiśnicki about the fixed point theory of monotone nonexpansive mappings. In their work, it is claimed that most of the fixed point results of this class of mappings boil down to the classical Knaster-Tarski fixed point theorem. We will show that their approach is very restrictive and fail to have any meaningful usefulness in applications.</p></abstract>

The purpose of this note is to discuss the recent paper of Espínola and Wiśnicki about the fixed point theory of monotone nonexpansive mappings. In their work, it is claimed that most of the fixed point results of this class of mappings boil down to the classical Knaster-Tarski fixed point theorem. We will show that their approach is very restrictive and fail to have any meaningful usefulness in applications.

Notes on Knaster-Tarski Theorem versus Monotone Nonexpansive Mappings

King Fahd University of Petroleum & Minerals

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The purpose of this note is to discuss the recent paper of Espínola and Wiśnicki about the fixed point theory of monotone nonexpansive mappings. In their work,...

Notes on Knaster-Tarski Theorem versus Monotone Nonexpansive Mappings

Online veröffentlicht: 01. Feb. 2019

Seitenbereich: 1 - 8

Eingereicht: 16. Aug. 2018

Akzeptiert: 15. Sept. 2018

DOI: https://doi.org/10.1515/mjpaa-2018-0001

Schlüsselwörter
Binary relation, Fixed point, integral delay equation, Krasnoselskii iteration, Lebesgue measure, monotone mapping, nonexpansive mapping, oriented graph, partially ordered

© 2018 Mohamed Amine Khamsi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Notes on Knaster-Tarski Theorem versus Monotone Nonexpansive Mappings

Online veröffentlicht: 01. Feb. 2019

Seitenbereich: 1 - 8

Eingereicht: 16. Aug. 2018

Akzeptiert: 15. Sept. 2018

DOI: https://doi.org/10.1515/mjpaa-2018-0001

SchlüsselwörterBinary relation, Fixed point, integral delay equation, Krasnoselskii iteration, Lebesgue measure, monotone mapping, nonexpansive mapping, oriented graph, partially ordered

© 2018 Mohamed Amine Khamsi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schlüsselwörter
Binary relation, Fixed point, integral delay equation, Krasnoselskii iteration, Lebesgue measure, monotone mapping, nonexpansive mapping, oriented graph, partially ordered