Approximate Fixed Points

Mostafa Bachar; Buthinah A. Bin Dehaish; Mohamed Amine Khamsi

doi:10.1016/B978-0-12-804295-3.50003-6

Approximate Fixed Points

Mostafa Bachar, Buthinah A. Bin Dehaish, Mohamed Amine Khamsi^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

3 Scopus citations

Abstract

In this chapter, we present some of the known results about the concept of approximate fixed points of a mapping. In particular, we discuss some new results on approximating fixed points of monotone mappings. Then we conclude this chapter with an application of these results to the case of a nonlinear semigroup of mappings. It is worth mentioning that approximate fixed points are useful when a computational approach is involved. In particular, most of the approximate fixed points discussed in this chapter are generated by an algorithm that allows its computational implementation.

Original language	English
Title of host publication	Fixed Point Theory and Graph Theory
Subtitle of host publication	Foundations and Integrative Approaches
Publisher	Elsevier Inc.
Pages	99-138
Number of pages	40
ISBN (Electronic)	9780128043653
ISBN (Print)	9780128042953
DOIs	https://doi.org/10.1016/B978-0-12-804295-3.50003-6
State	Published - 10 Jun 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc. All rights reserved.

Keywords

Approximate fixed points
Banach spaces
Hyperbolic spaces
Metric line
Monotone contraction mapping
Monotone mappings
Monotone nonexpansive mapping
Monotone nonlinear semigroups
Nonlinear semigroups

ASJC Scopus subject areas

General Mathematics

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10.1016/B978-0-12-804295-3.50003-6

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AU - Bin Dehaish, Buthinah A.

AU - Khamsi, Mohamed Amine

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N2 - In this chapter, we present some of the known results about the concept of approximate fixed points of a mapping. In particular, we discuss some new results on approximating fixed points of monotone mappings. Then we conclude this chapter with an application of these results to the case of a nonlinear semigroup of mappings. It is worth mentioning that approximate fixed points are useful when a computational approach is involved. In particular, most of the approximate fixed points discussed in this chapter are generated by an algorithm that allows its computational implementation.

AB - In this chapter, we present some of the known results about the concept of approximate fixed points of a mapping. In particular, we discuss some new results on approximating fixed points of monotone mappings. Then we conclude this chapter with an application of these results to the case of a nonlinear semigroup of mappings. It is worth mentioning that approximate fixed points are useful when a computational approach is involved. In particular, most of the approximate fixed points discussed in this chapter are generated by an algorithm that allows its computational implementation.

KW - Approximate fixed points

KW - Banach spaces

KW - Hyperbolic spaces

KW - Metric line

KW - Monotone contraction mapping

KW - Monotone mappings

KW - Monotone nonexpansive mapping

KW - Monotone nonlinear semigroups

KW - Nonlinear semigroups

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M3 - Chapter

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SN - 9780128042953

SP - 99

EP - 138

BT - Fixed Point Theory and Graph Theory

PB - Elsevier Inc.

ER -

Approximate Fixed Points

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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