On solving the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings

We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered pro...

Full description

Saved in:
Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2018; no. 1; pp. 1 - 17
Main Authors: Phuengrattana, Withun, Lerkchaiyaphum, Kritsada
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2018
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Differential Geometry
Fixed point problems
Hilbert spaces
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Nonexpansive multivalued mapping
Split generalized equilibrium problems
Topology
47H10
65K15
Nonexpansive multivalued mapping
47H09
Hilbert spaces
65K10
Fixed point problems
Split generalized equilibrium problems
ISSN:1687-1812, 1687-1812
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.
AbstractList Abstract We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.
We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.
ArticleNumber 6
Author Phuengrattana, Withun
Lerkchaiyaphum, Kritsada
Author_xml – sequence: 1
  givenname: Withun
  surname: Phuengrattana
  fullname: Phuengrattana, Withun
  email: withun_ph@yahoo.com
  organization: Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University, Research Center for Pure and Applied Mathematics, Research and Development Institute, Nakhon Pathom Rajabhat University
– sequence: 2
  givenname: Kritsada
  surname: Lerkchaiyaphum
  fullname: Lerkchaiyaphum, Kritsada
  organization: Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University
BookMark eNp9kc1u3SAQhVGVSk3SPkB3vIBbBmxsL6uoP5EiZZOu0RiPb7nC4IJ9lfQZ-tDl5jZVlUVWoOF8R4c5F-wsxECMvQfxAaDTHzMorVUloKuEVlDpV-wcdNdW0IE8--_-hl3kvBdC9o2oz9nv28Bz9AcXdnz9QTwv3q18R4ESeveLRk4_N-fdkNw28yXFwdPMMYyP6sndF8USXVj_vU0xceQ2bmHFMuATzs4_8DjxY-T7BUN2B-Lz5ld3QL8VgxmXpQTIb9nrCX2md3_PS_b9y-e7q2_Vze3X66tPN5VVIHXV2LprhtqO0PXD0Jb_o5ZKqVa3gxbUjj2RFG2LSHUvmxGILKhegLVilDWqS3Z98h0j7s2S3IzpwUR05nEQ085gWp31ZGiwtW06PU3S1i0C9p0CTdPYDWWloi9e7cnLpphzoslYt-LqYlgTOm9AmGNB5lSQKQWZY0FGFxKekU9JXmLkiclFG3aUzD5uKZRlvQD9ARA9qDI
CitedBy_id crossref_primary_10_3390_math11194175
crossref_primary_10_1186_s13660_022_02883_0
crossref_primary_10_1007_s40314_022_02136_2
crossref_primary_10_1007_s10013_021_00485_9
crossref_primary_10_1007_s12215_025_01213_9
crossref_primary_10_3846_mma_2023_17087
crossref_primary_10_1080_00207160_2020_1856823
Cites_doi 10.1155/2010/383740
10.1186/s13663-016-0509-4
10.1155/2010/582475
10.1007/BF02614504
10.1016/S0022-247X(02)00458-4
10.1016/j.camwa.2011.09.018
10.1186/s13663-015-0281-x
10.1090/conm/568/11285
10.22436/jnsa.009.04.07
10.1186/2251-7456-7-1
10.1090/S0002-9904-1967-11761-0
10.1007/s10852-014-9261-0
10.1016/j.jmaa.2005.03.002
10.1155/JAMSA.2005.323
10.1016/j.cam.2007.02.022
10.1007/s11075-011-9490-5
10.1155/2010/349158
10.1007/s10957-011-9814-6
10.1016/j.jmaa.2007.09.062
10.1016/j.na.2005.08.018
ContentType Journal Article
Copyright The Author(s) 2018
Copyright_xml – notice: The Author(s) 2018
DBID C6C
AAYXX
CITATION
DOA
DOI 10.1186/s13663-018-0631-6
DatabaseName Springer Nature OA Free Journals
CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList

Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1687-1812
EndPage 17
ExternalDocumentID oai_doaj_org_article_ebc4c586ff2c47a1a98316efd8b16809
10_1186_s13663_018_0631_6
GroupedDBID -A0
0R~
29H
2WC
3V.
4.4
40G
5GY
5VS
8FE
8FG
8R4
8R5
ABDBF
ABJCF
ACGFS
ACIPV
ACIWK
ACUHS
ADBBV
ADINQ
AENEX
AFKRA
AHBYD
AHYZX
ALMA_UNASSIGNED_HOLDINGS
AMKLP
ARAPS
BCNDV
BENPR
BPHCQ
C24
C6C
CS3
DU5
E3Z
EBS
EJD
ESX
GROUPED_DOAJ
HCIFZ
I-F
J9A
K6V
K7-
KQ8
L6V
M0N
M7S
OK1
P2P
P62
PIMPY
PQQKQ
PROAC
Q2X
REM
RHU
RNS
RSV
SMT
SOJ
TUS
U2A
UPT
~8M
AAYXX
CITATION
OVT
ID FETCH-LOGICAL-c3126-5c485b4cd189bb7118a62333767b60e7d9ee2077aae4925d1eec13901cc0d24a3
IEDL.DBID DOA
ISSN 1687-1812
IngestDate Fri Oct 03 12:51:35 EDT 2025
Tue Nov 18 22:37:51 EST 2025
Sat Nov 29 03:00:56 EST 2025
Fri Feb 21 02:36:30 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Keywords 47H10
65K15
Nonexpansive multivalued mapping
47H09
Hilbert spaces
65K10
Fixed point problems
Split generalized equilibrium problems
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c3126-5c485b4cd189bb7118a62333767b60e7d9ee2077aae4925d1eec13901cc0d24a3
OpenAccessLink https://doaj.org/article/ebc4c586ff2c47a1a98316efd8b16809
PageCount 17
ParticipantIDs doaj_primary_oai_doaj_org_article_ebc4c586ff2c47a1a98316efd8b16809
crossref_citationtrail_10_1186_s13663_018_0631_6
crossref_primary_10_1186_s13663_018_0631_6
springer_journals_10_1186_s13663_018_0631_6
PublicationCentury 2000
PublicationDate 20180301
PublicationDateYYYYMMDD 2018-03-01
PublicationDate_xml – month: 3
  year: 2018
  text: 20180301
  day: 1
PublicationDecade 2010
PublicationPlace Cham
PublicationPlace_xml – name: Cham
PublicationTitle Fixed point theory and applications (Hindawi Publishing Corporation)
PublicationTitleAbbrev Fixed Point Theory Appl
PublicationYear 2018
Publisher Springer International Publishing
SpringerOpen
Publisher_xml – name: Springer International Publishing
– name: SpringerOpen
References Suantai, Cholamjiak, Cho, Cholamjiak (CR15) 2016; 2016
Suantai (CR18) 2005; 311
Censor, Gibali, Reich (CR5) 2012; 59
Reich, Sabach (CR6) 2012; 56
Moudafi (CR10) 2011; 150
Cholamjiak, Suantai (CR21) 2010; 2010
Deepho, Martinez-Moreno, Kumam (CR9) 2016; 9
Byrne, Censor, Gibali, Reich (CR26) 2012; 13
Kimura (CR14) 2010; 2010
Ceng, Yao (CR1) 2008; 214
Zegeye, Shahzad (CR17) 2011; 62
Kimura, Nakajo, Takahashi (CR13) 2008; 9
Khan (CR20) 2005; 3
Opial (CR16) 1967; 73
Deepho, Kumam, Kumam (CR8) 2014; 13
Combettes, Hirstoaga (CR3) 2005; 6
Goebel, Reich (CR23) 1984
Cianciaruso, Marino, Muglia, Yao (CR11) 2010; 2010
Martinez-Yanesa, Xu (CR22) 2006; 64
Blum, Oettli (CR2) 1994; 63
Nakajo, Takahashi (CR24) 2003; 279
Flam, Antipin (CR4) 1997; 78
Takahashi, Takeuchi, Kubota (CR12) 2008; 341
Kazmi, Rizvi (CR7) 2013; 7
Iiduka, Takahashi (CR19) 2006; 7
Ma, Wang, Chang, Duan (CR25) 2015; 2015
S. Reich (631_CR6) 2012; 56
K.R. Kazmi (631_CR7) 2013; 7
K. Nakajo (631_CR24) 2003; 279
A.R. Khan (631_CR20) 2005; 3
Z. Ma (631_CR25) 2015; 2015
Y. Censor (631_CR5) 2012; 59
Z. Opial (631_CR16) 1967; 73
J. Deepho (631_CR9) 2016; 9
C. Byrne (631_CR26) 2012; 13
W. Takahashi (631_CR12) 2008; 341
W. Cholamjiak (631_CR21) 2010; 2010
A. Moudafi (631_CR10) 2011; 150
L.C. Ceng (631_CR1) 2008; 214
S.D. Flam (631_CR4) 1997; 78
Y. Kimura (631_CR14) 2010; 2010
S. Suantai (631_CR18) 2005; 311
Y. Kimura (631_CR13) 2008; 9
J. Deepho (631_CR8) 2014; 13
F. Cianciaruso (631_CR11) 2010; 2010
H. Iiduka (631_CR19) 2006; 7
K. Goebel (631_CR23) 1984
S. Suantai (631_CR15) 2016; 2016
P.I. Combettes (631_CR3) 2005; 6
E. Blum (631_CR2) 1994; 63
H. Zegeye (631_CR17) 2011; 62
C. Martinez-Yanesa (631_CR22) 2006; 64
References_xml – volume: 6
  start-page: 117
  year: 2005
  end-page: 136
  ident: CR3
  article-title: Equilibrium programming in Hilbert spaces
  publication-title: J. Nonlinear Convex Anal.
– volume: 7
  start-page: 105
  year: 2006
  end-page: 113
  ident: CR19
  article-title: Weak convergence theorem by Cesàro means for nonexpansive mappings and inverse-strongly monotone mappings
  publication-title: J. Nonlinear Convex Anal.
– year: 1984
  ident: CR23
  publication-title: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings
– volume: 2010
  year: 2010
  ident: CR11
  article-title: A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem
  publication-title: Fixed Point Theory Appl.
  doi: 10.1155/2010/383740
– volume: 2016
  year: 2016
  ident: CR15
  article-title: On solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert spaces
  publication-title: Fixed Point Theory Appl.
  doi: 10.1186/s13663-016-0509-4
– volume: 63
  start-page: 123
  year: 1994
  end-page: 145
  ident: CR2
  article-title: From optimization and variational inequalities to equilibrium problems
  publication-title: Math. Stud.
– volume: 2010
  year: 2010
  ident: CR14
  article-title: Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball
  publication-title: Abstr. Appl. Anal.
  doi: 10.1155/2010/582475
– volume: 78
  start-page: 29
  year: 1997
  end-page: 41
  ident: CR4
  article-title: Equilibrium programming using proximal-like algorithm
  publication-title: Math. Program.
  doi: 10.1007/BF02614504
– volume: 279
  start-page: 372
  year: 2003
  end-page: 379
  ident: CR24
  article-title: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/S0022-247X(02)00458-4
– volume: 62
  start-page: 4007
  year: 2011
  end-page: 4014
  ident: CR17
  article-title: Convergence of Mann’s type iteration method for generalized asymptotically nonexpansive mappings
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2011.09.018
– volume: 2015
  year: 2015
  ident: CR25
  article-title: Convergence theorems for split equality mixed equilibrium problems with applications
  publication-title: Fixed Point Theory Appl.
  doi: 10.1186/s13663-015-0281-x
– volume: 56
  start-page: 225
  year: 2012
  end-page: 240
  ident: CR6
  article-title: Three strong convergence theorems regarding iterative methods for solving equilibrium problems in reflexive Banach spaces
  publication-title: Contemp. Math.
  doi: 10.1090/conm/568/11285
– volume: 9
  start-page: 1475
  year: 2016
  end-page: 1496
  ident: CR9
  article-title: A viscosity of Cesàro mean approximation method for split generalized equilibrium, variational inequality and fixed point problems
  publication-title: J. Nonlinear Sci. Appl.
  doi: 10.22436/jnsa.009.04.07
– volume: 7
  year: 2013
  ident: CR7
  article-title: Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup
  publication-title: Math. Sci.
  doi: 10.1186/2251-7456-7-1
– volume: 9
  start-page: 407
  year: 2008
  end-page: 416
  ident: CR13
  article-title: Strongly convergent iterative schemes for a sequence of nonlinear mappings
  publication-title: J. Nonlinear Convex Anal.
– volume: 73
  start-page: 591
  year: 1967
  end-page: 597
  ident: CR16
  article-title: Weak convergence of the sequence of successive approximation for nonexpansive mappings
  publication-title: Bull. Am. Math. Soc.
  doi: 10.1090/S0002-9904-1967-11761-0
– volume: 13
  start-page: 405
  issue: 4
  year: 2014
  end-page: 423
  ident: CR8
  article-title: A new hybrid projection algorithm for solving the split generalized equilibrium problems and the system of variational inequality problems
  publication-title: J. Math. Model. Algorithms Oper. Res.
  doi: 10.1007/s10852-014-9261-0
– volume: 311
  start-page: 506
  year: 2005
  end-page: 517
  ident: CR18
  article-title: Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2005.03.002
– volume: 3
  start-page: 323
  year: 2005
  end-page: 331
  ident: CR20
  article-title: Properties of fixed point set of a multivalued map
  publication-title: J. Appl. Math. Stoch. Anal.
  doi: 10.1155/JAMSA.2005.323
– volume: 214
  start-page: 186
  year: 2008
  end-page: 201
  ident: CR1
  article-title: A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/j.cam.2007.02.022
– volume: 59
  start-page: 301
  year: 2012
  end-page: 323
  ident: CR5
  article-title: Algorithms for the split variational inequality problem
  publication-title: Numer. Algorithms
  doi: 10.1007/s11075-011-9490-5
– volume: 2010
  year: 2010
  ident: CR21
  article-title: A hybrid method for a countable family of multivalued maps, equilibrium problems, and variational inequality problems
  publication-title: Discrete Dyn. Nat. Soc.
  doi: 10.1155/2010/349158
– volume: 13
  start-page: 759
  issue: 4
  year: 2012
  end-page: 775
  ident: CR26
  article-title: The split common null point problem
  publication-title: J. Nonlinear Convex Anal.
– volume: 150
  start-page: 275
  year: 2011
  end-page: 283
  ident: CR10
  article-title: Split monotone variational inclusions
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-011-9814-6
– volume: 341
  start-page: 276
  year: 2008
  end-page: 286
  ident: CR12
  article-title: Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2007.09.062
– volume: 64
  start-page: 2400
  year: 2006
  end-page: 2411
  ident: CR22
  article-title: Strong convergence of the CQ method for fixed point iteration processes
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2005.08.018
– volume: 63
  start-page: 123
  year: 1994
  ident: 631_CR2
  publication-title: Math. Stud.
– volume: 9
  start-page: 407
  year: 2008
  ident: 631_CR13
  publication-title: J. Nonlinear Convex Anal.
– volume: 7
  start-page: 105
  year: 2006
  ident: 631_CR19
  publication-title: J. Nonlinear Convex Anal.
– volume: 73
  start-page: 591
  year: 1967
  ident: 631_CR16
  publication-title: Bull. Am. Math. Soc.
  doi: 10.1090/S0002-9904-1967-11761-0
– volume: 9
  start-page: 1475
  year: 2016
  ident: 631_CR9
  publication-title: J. Nonlinear Sci. Appl.
  doi: 10.22436/jnsa.009.04.07
– volume: 2010
  year: 2010
  ident: 631_CR14
  publication-title: Abstr. Appl. Anal.
  doi: 10.1155/2010/582475
– volume: 7
  year: 2013
  ident: 631_CR7
  publication-title: Math. Sci.
  doi: 10.1186/2251-7456-7-1
– volume: 6
  start-page: 117
  year: 2005
  ident: 631_CR3
  publication-title: J. Nonlinear Convex Anal.
– volume: 64
  start-page: 2400
  year: 2006
  ident: 631_CR22
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2005.08.018
– volume: 3
  start-page: 323
  year: 2005
  ident: 631_CR20
  publication-title: J. Appl. Math. Stoch. Anal.
  doi: 10.1155/JAMSA.2005.323
– volume: 311
  start-page: 506
  year: 2005
  ident: 631_CR18
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2005.03.002
– volume-title: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings
  year: 1984
  ident: 631_CR23
– volume: 56
  start-page: 225
  year: 2012
  ident: 631_CR6
  publication-title: Contemp. Math.
  doi: 10.1090/conm/568/11285
– volume: 13
  start-page: 759
  issue: 4
  year: 2012
  ident: 631_CR26
  publication-title: J. Nonlinear Convex Anal.
– volume: 78
  start-page: 29
  year: 1997
  ident: 631_CR4
  publication-title: Math. Program.
  doi: 10.1007/BF02614504
– volume: 2010
  year: 2010
  ident: 631_CR21
  publication-title: Discrete Dyn. Nat. Soc.
  doi: 10.1155/2010/349158
– volume: 150
  start-page: 275
  year: 2011
  ident: 631_CR10
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-011-9814-6
– volume: 2010
  year: 2010
  ident: 631_CR11
  publication-title: Fixed Point Theory Appl.
  doi: 10.1155/2010/383740
– volume: 13
  start-page: 405
  issue: 4
  year: 2014
  ident: 631_CR8
  publication-title: J. Math. Model. Algorithms Oper. Res.
  doi: 10.1007/s10852-014-9261-0
– volume: 59
  start-page: 301
  year: 2012
  ident: 631_CR5
  publication-title: Numer. Algorithms
  doi: 10.1007/s11075-011-9490-5
– volume: 2015
  year: 2015
  ident: 631_CR25
  publication-title: Fixed Point Theory Appl.
  doi: 10.1186/s13663-015-0281-x
– volume: 341
  start-page: 276
  year: 2008
  ident: 631_CR12
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2007.09.062
– volume: 214
  start-page: 186
  year: 2008
  ident: 631_CR1
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/j.cam.2007.02.022
– volume: 62
  start-page: 4007
  year: 2011
  ident: 631_CR17
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2011.09.018
– volume: 2016
  year: 2016
  ident: 631_CR15
  publication-title: Fixed Point Theory Appl.
  doi: 10.1186/s13663-016-0509-4
– volume: 279
  start-page: 372
  year: 2003
  ident: 631_CR24
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/S0022-247X(02)00458-4
SSID ssj0029504
Score 2.166677
Snippet We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert...
Abstract We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real...
SourceID doaj
crossref
springer
SourceType Open Website
Enrichment Source
Index Database
Publisher
StartPage 1
SubjectTerms Analysis
Applications of Mathematics
Differential Geometry
Fixed point problems
Hilbert spaces
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Nonexpansive multivalued mapping
Split generalized equilibrium problems
Topology
Title On solving the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings
URI https://link.springer.com/article/10.1186/s13663-018-0631-6
https://doaj.org/article/ebc4c586ff2c47a1a98316efd8b16809
Volume 2018
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 1687-1812
  dateEnd: 20201231
  omitProxy: false
  ssIdentifier: ssj0029504
  issn: 1687-1812
  databaseCode: DOA
  dateStart: 20040101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lb9QwELaqVQ_lgCgFsZQiHzgVRY1jx48joFZcWDi0Um-WH5MqEpttm1206m_oj8bjZFetKuDC1ZnE0cyXeGY8_oaQDxp0DbL0BeioCsFSgOKwyDGWBqQ0uongcrMJNZvpy0vz40GrL6wJG-iBB8WdgA8i1Fo2TRWEcswZzZmEJmrPpB6O7pXKbIKpMdQydSnGPUym5UnPuMT9SqaLtCSzQj5ahTJZ_5Od0LzAnL0gz0fPkH4a3mif7ED3kjz7tqVV7Q_I_feOJqxgDoCmYdonD3JJrwbm6PYOIoWbVZur-FdzOvaKoa6LWbpp10nietF2y-215LJSR3PDCDxDRYd8B100tFt0sE6_Cixvp7nsEHnB0wPmDikdrvpX5OLs9PzL12Jsp1AEzipZ1EHo2osQmTbeq6QYl3wfjnQuXpagogFIqlTOATIWRgYQGKZEQihjJRx_TSY49xtCq5jsAY57HrlwhmthpGpME3w0ARSfknKjXhtGrnFsefHT5phDSztYxCaLWLSIlVNyvL3leiDa-JvwZ7TZVhA5svNAQo4dkWP_hZwp-bixuB0_3P7PU779H1Mekr0qgxCx-I5MlrcrOCK74dey7W_fZwj_BmSv91Y
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+solving+the+split+generalized+equilibrium+problem+and+the+fixed+point+problem+for+a+countable+family+of+nonexpansive+multivalued+mappings&rft.jtitle=Fixed+point+theory+and+applications+%28Hindawi+Publishing+Corporation%29&rft.au=Withun+Phuengrattana&rft.au=Kritsada+Lerkchaiyaphum&rft.date=2018-03-01&rft.pub=SpringerOpen&rft.eissn=1687-1812&rft.volume=2018&rft.issue=1&rft.spage=1&rft.epage=17&rft_id=info:doi/10.1186%2Fs13663-018-0631-6&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_ebc4c586ff2c47a1a98316efd8b16809
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1687-1812&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1687-1812&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1687-1812&client=summon