On monotone mappings in modular function spaces

Buthinah A. Bin Dehaish; Mohamed A. Khamsi

doi:10.22436/jnsa.009.08.07

On monotone mappings in modular function spaces

Buthinah A. Bin Dehaish, Mohamed A. Khamsi

Mathematics

King Abdulaziz University

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

6 Scopus citations

Abstract

We prove the existence of fixed points of monotone ρ-nonexpansive mappings in ρ-uniformly convex modular function spaces. This is the modular version of Browder and Göhde fixed point theorems for monotone mappings. We also discuss the validity of this result in modular function spaces where the modular is uniformly convex in every direction. This property has never been considered in the context of modular spaces.

Original language	British English
Pages (from-to)	5219-5228
Number of pages	10
Journal	Journal of Nonlinear Science and Applications
Volume	9
Issue number	8
DOIs	https://doi.org/10.22436/jnsa.009.08.07
State	Published - 2016

Keywords

Fixed point
Krasnoselskii iteration
Modular function spaces
Monotone mapping
Nonexpansive mapping
Partially ordered
Uniformly convex
Uniformly convex in every direction

Access to Document

10.22436/jnsa.009.08.07

Cite this

@article{f7cc52c3ca8f478abb8cf5259d9433d8,

title = "On monotone mappings in modular function spaces",

abstract = "We prove the existence of fixed points of monotone ρ-nonexpansive mappings in ρ-uniformly convex modular function spaces. This is the modular version of Browder and G{\"o}hde fixed point theorems for monotone mappings. We also discuss the validity of this result in modular function spaces where the modular is uniformly convex in every direction. This property has never been considered in the context of modular spaces.",

keywords = "Fixed point, Krasnoselskii iteration, Modular function spaces, Monotone mapping, Nonexpansive mapping, Partially ordered, Uniformly convex, Uniformly convex in every direction",

author = "{Bin Dehaish}, {Buthinah A.} and Khamsi, {Mohamed A.}",

note = "Funding Information: This work is supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (363-59-D1436). The authors, therefore, gratefully acknowledge the DSR technical and financial support. Publisher Copyright: {\textcopyright} 2016 All rights reserved.",

year = "2016",

doi = "10.22436/jnsa.009.08.07",

language = "British English",

volume = "9",

pages = "5219--5228",

journal = "Journal of Nonlinear Science and Applications",

issn = "2008-1898",

publisher = "International Scientific Research Publications",

number = "8",

}

TY - JOUR

T1 - On monotone mappings in modular function spaces

AU - Bin Dehaish, Buthinah A.

AU - Khamsi, Mohamed A.

N1 - Funding Information: This work is supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (363-59-D1436). The authors, therefore, gratefully acknowledge the DSR technical and financial support. Publisher Copyright: © 2016 All rights reserved.

PY - 2016

Y1 - 2016

N2 - We prove the existence of fixed points of monotone ρ-nonexpansive mappings in ρ-uniformly convex modular function spaces. This is the modular version of Browder and Göhde fixed point theorems for monotone mappings. We also discuss the validity of this result in modular function spaces where the modular is uniformly convex in every direction. This property has never been considered in the context of modular spaces.

AB - We prove the existence of fixed points of monotone ρ-nonexpansive mappings in ρ-uniformly convex modular function spaces. This is the modular version of Browder and Göhde fixed point theorems for monotone mappings. We also discuss the validity of this result in modular function spaces where the modular is uniformly convex in every direction. This property has never been considered in the context of modular spaces.

KW - Fixed point

KW - Krasnoselskii iteration

KW - Modular function spaces

KW - Monotone mapping

KW - Nonexpansive mapping

KW - Partially ordered

KW - Uniformly convex

KW - Uniformly convex in every direction

UR - http://www.scopus.com/inward/record.url?scp=84994029429&partnerID=8YFLogxK

U2 - 10.22436/jnsa.009.08.07

DO - 10.22436/jnsa.009.08.07

M3 - Article

AN - SCOPUS:84994029429

SN - 2008-1898

VL - 9

SP - 5219

EP - 5228

JO - Journal of Nonlinear Science and Applications

JF - Journal of Nonlinear Science and Applications

IS - 8

ER -

On monotone mappings in modular function spaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this