A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications

Shih Sen Chang; Heung Wing Joseph Lee; Chi Kin Chan

doi:10.1016/j.na.2010.06.006

A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications

Shih Sen Chang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publication › Journal article › Academic research › peer-review

56 Citations (Scopus)

Abstract

The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.

Original language	English
Pages (from-to)	2260-2270
Number of pages	11
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	73
Issue number	7
DOIs	https://doi.org/10.1016/j.na.2010.06.006
Publication status	Published - 1 Oct 2010

Keywords

α-inverse- strongly monotone mapping
Equilibrium problem
Generalized equilibrium problem
Maximal monotone operator
Relatively nonexpansive mapping
Variational inequality

ASJC Scopus subject areas

Analysis
Applied Mathematics

More information

10.1016/j.na.2010.06.006

Cite this

@article{9c10dee6dbda4474ada2823e897f2037,

title = "A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications",

abstract = "The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.",

keywords = "α-inverse- strongly monotone mapping, Equilibrium problem, Generalized equilibrium problem, Maximal monotone operator, Relatively nonexpansive mapping, Variational inequality",

author = "Chang, {Shih Sen} and Lee, {Heung Wing Joseph} and Chan, {Chi Kin}",

year = "2010",

month = oct,

day = "1",

doi = "10.1016/j.na.2010.06.006",

language = "English",

volume = "73",

pages = "2260--2270",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd",

number = "7",

}

A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications. / Chang, Shih Sen; Lee, Heung Wing Joseph; Chan, Chi Kin.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 73, No. 7, 01.10.2010, p. 2260-2270.

Research output: Journal article publication › Journal article › Academic research › peer-review

TY - JOUR

T1 - A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications

AU - Chang, Shih Sen

AU - Lee, Heung Wing Joseph

AU - Chan, Chi Kin

PY - 2010/10/1

Y1 - 2010/10/1

N2 - The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.

AB - The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.

KW - α-inverse- strongly monotone mapping

KW - Equilibrium problem

KW - Generalized equilibrium problem

KW - Maximal monotone operator

KW - Relatively nonexpansive mapping

KW - Variational inequality

UR - http://www.scopus.com/inward/record.url?scp=77955415280&partnerID=8YFLogxK

U2 - 10.1016/j.na.2010.06.006

DO - 10.1016/j.na.2010.06.006

M3 - Journal article

SN - 0362-546X

VL - 73

SP - 2260

EP - 2270

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 7

ER -

A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this