On monotone nonexpansive mappings in L1([0,1])

Mohamed Amine Khamsi; Abdul Rahim Khan

doi:10.1186/s13663-015-0346-x

On monotone nonexpansive mappings in L₁([0,1])

Mohamed Amine Khamsi, Abdul Rahim Khan^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Let the set C⊂L1([0,1]) be nonempty, convex and compact for the convergence almost everywhere and T:C→C be a monotone nonexpansive mapping. In this paper, we study the behavior of the Krasnoselskii-Ishikawa iteration sequence {fn} defined by fn+1=λfn+(1−λ)T(fn), n=1,2,…, λ∈(0,1). Then we prove a fixed point theorem for these mappings. Our result is new and was never investigated.

Original language	English
Article number	94
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13663-015-0346-x
State	Published - 26 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015, Khamsi and Khan.

Keywords

Ishikawa iteration
Krasnoselskii iteration
Lebesgue measure
convergence almost everywhere
fixed point
monotone mapping
nonexpansive mapping

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

Access to Document

10.1186/s13663-015-0346-x

Cite this

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AB - Let the set C⊂L1([0,1]) be nonempty, convex and compact for the convergence almost everywhere and T:C→C be a monotone nonexpansive mapping. In this paper, we study the behavior of the Krasnoselskii-Ishikawa iteration sequence {fn} defined by fn+1=λfn+(1−λ)T(fn), n=1,2,…, λ∈(0,1). Then we prove a fixed point theorem for these mappings. Our result is new and was never investigated.

KW - Ishikawa iteration

KW - Krasnoselskii iteration

KW - Lebesgue measure

KW - convergence almost everywhere

KW - fixed point

KW - monotone mapping

KW - nonexpansive mapping

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