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

Mathematics

King Fahd University for Petroleum and Minerals (KFUPM)

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	British English
Article number	94
Journal	Fixed Point Theory and Applications
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13663-015-0346-x
State	Published - 26 Dec 2015

Keywords

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

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10.1186/s13663-015-0346-x

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

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.",

keywords = "convergence almost everywhere, fixed point, Ishikawa iteration, Krasnoselskii iteration, Lebesgue measure, monotone mapping, nonexpansive mapping",

author = "Khamsi, {Mohamed Amine} and Khan, {Abdul Rahim}",

note = "Funding Information: The authors acknowledge gratefully the support of KACST, Riyad, Saudi Arabia, for supporting Research Project ARP-32-34. Publisher Copyright: {\textcopyright} 2015, Khamsi and Khan.",

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AU - Khan, Abdul Rahim

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N2 - 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.

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.

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KW - fixed point

KW - Ishikawa iteration

KW - Krasnoselskii iteration

KW - Lebesgue measure

KW - monotone mapping

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

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Keywords

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