Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems

In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-ad...

Full description

Saved in:
Bibliographic Details
Published inOptimization Vol. 72; no. 3; pp. 677 - 711
Main Authors Ogwo, G. N., Alakoya, T. O., Mewomo, O. T.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 04.03.2023
Taylor & Francis LLC
Subjects
Adaptive algorithms
fixed point problem
Half spaces
Hilbert space
Iterative algorithms
Iterative methods
iterative scheme
Lipschitzian
Mathematical analysis
Minimization problem
Operators (mathematics)
quasi-pseudocontractive mappings
Online AccessGet full text

Cover

Abstract In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-adaptive step size. We prove that the sequence generated by our proposed methods converges strongly to a common solution of the VIP and FPP of an infinite family of strict pseudo-contractive mappings in Hilbert spaces under some mild assumptions when the underlying operator is monotone and Lipschitz continuous. Furthermore, we apply our results to find a common solution of VIP and zero-point problem (ZPP) for an infinite family of maximal monotone operators. Finally, we provide some numerical experiments of the proposed methods in comparison with other existing methods in the literature.
AbstractList In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-adaptive step size. We prove that the sequence generated by our proposed methods converges strongly to a common solution of the VIP and FPP of an infinite family of strict pseudo-contractive mappings in Hilbert spaces under some mild assumptions when the underlying operator is monotone and Lipschitz continuous. Furthermore, we apply our results to find a common solution of VIP and zero-point problem (ZPP) for an infinite family of maximal monotone operators. Finally, we provide some numerical experiments of the proposed methods in comparison with other existing methods in the literature.
Author Ogwo, G. N.
Alakoya, T. O.
Mewomo, O. T.
Author_xml – sequence: 1
  givenname: G. N.
  surname: Ogwo
  fullname: Ogwo, G. N.
  organization: University of KwaZulu-Natal
– sequence: 2
  givenname: T. O.
  surname: Alakoya
  fullname: Alakoya, T. O.
  organization: University of KwaZulu-Natal
– sequence: 3
  givenname: O. T.
  surname: Mewomo
  fullname: Mewomo, O. T.
  email: mewomoo@ukzn.ac.za
  organization: University of KwaZulu-Natal
BookMark eNqFkN1OHCEYhkljk662l9CExONZ-Zl1hvREY2zdxKQn7TH5luFTDAMjsOp6B73rMq498aCe8BOe9wWeQ3IQYrCEfOVsyVnPTpiQkivZLgUTfMlVz3vVfSALzoRqWtWuDshiZpoZ-kQOc75jlTwV7YL8WReboLgHS8HfxOTK7Ugf60iz9djAANPLYS52otk9W4oxUZimFJ_cWIPhhpZbS00cxxhojn5bXF1EpA-QHMwb8NQFe78F78qOQhgouic70Cm6UGht2ng75s_kI4LP9svrfER-f7_8dXHVXP_8sb44v26MlH1pekQrEZAbAImtQbXphk61RnRsJTYdIhdCKmOBc7AIG8kqqnrZoujhdJBH5HjfWy--39pc9F3cpvrIrEXXM8mY4qxSqz1lUsw5WdRTqv9NO82Znq3rf9b1bF2_Wq-5b29yxpUXCyWB8--mz_ZpF6rmER5j8oMusPMxYYJgXNby_xV_ASOfobA
CitedBy_id crossref_primary_10_1017_S0013091523000251
crossref_primary_10_1142_S1793557122502011
crossref_primary_10_1142_S179355712250139X
crossref_primary_10_1515_jaa_2022_2010
crossref_primary_10_1007_s41980_022_00678_z
crossref_primary_10_3390_math13010133
crossref_primary_10_3934_jimo_2021210
crossref_primary_10_3934_jimo_2024184
crossref_primary_10_24193_subbmath_2024_3_12
crossref_primary_10_1186_s13660_022_02782_4
crossref_primary_10_1007_s40314_024_02829_w
crossref_primary_10_1080_02331934_2023_2168482
crossref_primary_10_1515_taa_2022_0124
crossref_primary_10_3934_math_2023651
crossref_primary_10_1007_s40590_021_00408_1
crossref_primary_10_1007_s40314_021_01749_3
crossref_primary_10_1080_02331934_2022_2069022
crossref_primary_10_30755_NSJOM_14084
crossref_primary_10_1007_s40306_022_00480_3
crossref_primary_10_1186_s13660_023_03043_8
crossref_primary_10_1515_math_2022_0030
crossref_primary_10_3934_math_2024629
crossref_primary_10_1007_s40314_023_02209_w
crossref_primary_10_3390_math11020386
crossref_primary_10_1007_s10473_022_0501_5
crossref_primary_10_1515_cmam_2022_0199
crossref_primary_10_1007_s40314_022_02138_0
crossref_primary_10_1515_dema_2022_0005
crossref_primary_10_1186_s13660_022_02805_0
crossref_primary_10_1007_s40314_023_02555_9
crossref_primary_10_1002_mma_8849
crossref_primary_10_1016_j_knosys_2024_112550
Cites_doi 10.1007/s11075-021-01081-1
10.3934/jimo.2020152
10.1142/S1793557121501370
10.1137/060675319
10.1137/050626090
10.1007/s11075-020-00937-2
10.1080/02331934.2020.1789129
10.1016/j.camwa.2007.03.012
10.3934/naco.2021004
10.1023/A:1025407607560
10.1007/s11075-016-0253-1
10.1007/s40574-020-00272-3
10.1080/02331934.2020.1808648
10.1016/0041-5553(64)90137-5
10.1016/j.aml.2010.12.048
10.1016/j.na.2007.05.032
10.3390/math7100925
10.1016/j.na.2008.04.035
10.1007/s11075-011-9490-5
10.3934/naco.2021011
10.1080/02331934.2021.1895154
10.11650/twjm/1500407345
10.1007/978-3-642-56468-0
10.1007/s13370-020-00869-z
10.1080/10556788.2010.551536
10.1007/s11081-020-09593-w
10.1109/TSP.2003.812846
10.1515/dema-2021-0006
10.1007/s10957-005-7564-z
10.1080/02331934.2010.539689
10.24193/fpt-ro.2020.1.07
10.1007/s11075-018-0504-4
10.24193/fpt-ro.2018.2.39
10.1007/BF01581204
10.3390/math7100881
10.1090/S0002-9904-1967-11761-0
10.1007/s12190-009-0233-x
10.1186/s13660-019-2229-x
10.1007/s11075-017-0412-z
10.1007/s11565-020-00354-2
ContentType Journal Article
Copyright 2021 Informa UK Limited, trading as Taylor & Francis Group 2021
2021 Informa UK Limited, trading as Taylor & Francis Group
Copyright_xml – notice: 2021 Informa UK Limited, trading as Taylor & Francis Group 2021
– notice: 2021 Informa UK Limited, trading as Taylor & Francis Group
DBID AAYXX
CITATION
7SC
7TB
8FD
FR3
H8D
JQ2
L7M
L~C
L~D
DOI 10.1080/02331934.2021.1981897
DatabaseName CrossRef
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
Aerospace Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Aerospace Database
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList Aerospace Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1029-4945
EndPage 711
ExternalDocumentID 10_1080_02331934_2021_1981897
1981897
Genre Research Article
GroupedDBID .7F
.DC
.QJ
0BK
0R~
123
29N
30N
4.4
5VS
AAENE
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACGEJ
ACGFS
ACIWK
ACTIO
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AGDLA
AGMYJ
AHDZW
AIJEM
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AQRUH
AVBZW
AWYRJ
BLEHA
CCCUG
CE4
CS3
DKSSO
DU5
EBS
E~A
E~B
GTTXZ
H13
HF~
HZ~
H~P
IPNFZ
J.P
KYCEM
LJTGL
M4Z
NA5
O9-
P2P
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TTHFI
TUROJ
TWF
UT5
UU3
ZGOLN
~S~
AAGDL
AAHIA
AAYXX
ADYSH
AFRVT
AIYEW
AMPGV
AMVHM
CITATION
7SC
7TB
8FD
FR3
H8D
JQ2
L7M
L~C
L~D
TASJS
ID FETCH-LOGICAL-c338t-8ffe3faf1caa3f4cf9b7d794c27052b7ff12239cea11aefab301ca9834f28a6d3
ISSN 0233-1934
IngestDate Wed Aug 13 07:40:59 EDT 2025
Tue Jul 01 03:52:13 EDT 2025
Thu Apr 24 23:13:14 EDT 2025
Wed Dec 25 09:04:49 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 3
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c338t-8ffe3faf1caa3f4cf9b7d794c27052b7ff12239cea11aefab301ca9834f28a6d3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2780300910
PQPubID 27961
PageCount 35
ParticipantIDs crossref_primary_10_1080_02331934_2021_1981897
crossref_citationtrail_10_1080_02331934_2021_1981897
proquest_journals_2780300910
informaworld_taylorfrancis_310_1080_02331934_2021_1981897
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2023-03-04
PublicationDateYYYYMMDD 2023-03-04
PublicationDate_xml – month: 03
  year: 2023
  text: 2023-03-04
  day: 04
PublicationDecade 2020
PublicationPlace Philadelphia
PublicationPlace_xml – name: Philadelphia
PublicationTitle Optimization
PublicationYear 2023
Publisher Taylor & Francis
Taylor & Francis LLC
Publisher_xml – name: Taylor & Francis
– name: Taylor & Francis LLC
References CIT0030
CIT0032
CIT0031
CIT0033
Tian M (CIT0054) 2017; 1
Yao Y (CIT0022) 2007; 186
CIT0036
CIT0035
CIT0039
Korpelevich GM. (CIT0010) 1976; 12
Alakoya TO (CIT0019) 2021; 5
CIT0041
CIT0040
CIT0043
CIT0042
CIT0045
CIT0044
Ceng LC (CIT0034) 2019
Thong DV (CIT0023) 2019
CIT0003
CIT0047
CIT0002
CIT0005
CIT0049
CIT0004
CIT0048
CIT0007
CIT0006
CIT0009
CIT0008
CIT0050
CIT0052
Takahashi W. (CIT0046) 2000
CIT0053
CIT0012
Olona MA (CIT0038) 2021; 2021
CIT0011
Fichera G. (CIT0001) 1963; 34
Fan A (CIT0025) 2021; 5
CIT0014
CIT0013
CIT0016
CIT0015
CIT0018
CIT0017
CIT0020
Thong DV (CIT0021) 2018; 20
Aoyama K (CIT0051) 2007; 8
CIT0024
CIT0027
CIT0026
Shahazad N (CIT0037) 2014; 2014
CIT0029
CIT0028
References_xml – ident: CIT0005
  doi: 10.1007/s11075-021-01081-1
– ident: CIT0017
  doi: 10.3934/jimo.2020152
– ident: CIT0008
  doi: 10.1142/S1793557121501370
– ident: CIT0026
  doi: 10.1137/060675319
– ident: CIT0048
  doi: 10.1137/050626090
– ident: CIT0009
  doi: 10.1007/s11075-020-00937-2
– volume: 186
  start-page: 1551
  issue: 2
  year: 2007
  ident: CIT0022
  publication-title: Appl Math Comput
– ident: CIT0024
  doi: 10.1080/02331934.2020.1789129
– ident: CIT0053
  doi: 10.1016/j.camwa.2007.03.012
– volume-title: Nonlinear functional analysis-fixed point theory and its applications
  year: 2000
  ident: CIT0046
– ident: CIT0041
  doi: 10.3934/naco.2021004
– ident: CIT0027
  doi: 10.1023/A:1025407607560
– ident: CIT0002
– ident: CIT0015
  doi: 10.1007/s11075-016-0253-1
– ident: CIT0049
  doi: 10.1007/s40574-020-00272-3
– ident: CIT0007
  doi: 10.1080/02331934.2020.1808648
– volume: 2014
  year: 2014
  ident: CIT0037
  publication-title: Fixed Point Theory Appl
– ident: CIT0016
  doi: 10.1016/0041-5553(64)90137-5
– ident: CIT0042
  doi: 10.1016/j.aml.2010.12.048
– ident: CIT0035
  doi: 10.1016/j.na.2007.05.032
– volume: 34
  start-page: 138
  year: 1963
  ident: CIT0001
  publication-title: Atti Accad Naz Lincei VIII Ser Rend Cl Sci Fis Mat Nat
– ident: CIT0031
  doi: 10.3390/math7100925
– ident: CIT0044
  doi: 10.1016/j.na.2008.04.035
– ident: CIT0003
  doi: 10.1007/s11075-011-9490-5
– ident: CIT0004
  doi: 10.3934/naco.2021011
– ident: CIT0018
  doi: 10.1080/02331934.2021.1895154
– ident: CIT0043
  doi: 10.11650/twjm/1500407345
– ident: CIT0040
  doi: 10.1007/978-3-642-56468-0
– volume: 20
  start-page: 1
  issue: 4
  year: 2018
  ident: CIT0021
  publication-title: J Fixed Point Appl
– ident: CIT0006
  doi: 10.1007/s13370-020-00869-z
– volume: 12
  start-page: 747
  year: 1976
  ident: CIT0010
  publication-title: Ekon Mat Metody
– volume: 8
  start-page: 471
  year: 2007
  ident: CIT0051
  publication-title: J Nonlinear Convex Anal
– ident: CIT0012
  doi: 10.1080/10556788.2010.551536
– ident: CIT0020
  doi: 10.1007/s11081-020-09593-w
– ident: CIT0052
  doi: 10.1109/TSP.2003.812846
– ident: CIT0039
  doi: 10.1515/dema-2021-0006
– ident: CIT0028
  doi: 10.1007/s10957-005-7564-z
– ident: CIT0011
  doi: 10.1080/02331934.2010.539689
– volume: 2021
  year: 2021
  ident: CIT0038
  publication-title: J Nonlinear Funct Anal
– ident: CIT0029
  doi: 10.24193/fpt-ro.2020.1.07
– volume: 5
  start-page: 803
  year: 2021
  ident: CIT0019
  publication-title: J Nonlinear Var Anal
– start-page: 1
  year: 2019
  ident: CIT0034
  publication-title: Optimization
– ident: CIT0014
  doi: 10.1007/s11075-018-0504-4
– ident: CIT0030
  doi: 10.24193/fpt-ro.2018.2.39
– ident: CIT0050
  doi: 10.1007/BF01581204
– ident: CIT0033
  doi: 10.3390/math7100881
– ident: CIT0045
  doi: 10.1090/S0002-9904-1967-11761-0
– volume: 5
  start-page: 777
  year: 2021
  ident: CIT0025
  publication-title: J Nonlinear Var Anal
– ident: CIT0036
  doi: 10.1007/s12190-009-0233-x
– ident: CIT0032
  doi: 10.1186/s13660-019-2229-x
– ident: CIT0013
  doi: 10.1007/s11075-017-0412-z
– ident: CIT0047
  doi: 10.1007/s11565-020-00354-2
– volume: 1
  start-page: 1
  year: 2017
  ident: CIT0054
  publication-title: J Inequal Appl
– start-page: 1
  year: 2019
  ident: CIT0023
  publication-title: Optim Lett
SSID ssj0021624
Score 2.5020218
Snippet In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality...
SourceID proquest
crossref
informaworld
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 677
SubjectTerms Adaptive algorithms
fixed point problem
Half spaces
Hilbert space
Iterative algorithms
Iterative methods
iterative scheme
Lipschitzian
Mathematical analysis
Minimization problem
Operators (mathematics)
quasi-pseudocontractive mappings
Title Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems
URI https://www.tandfonline.com/doi/abs/10.1080/02331934.2021.1981897
https://www.proquest.com/docview/2780300910
Volume 72
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lj9MwELZK9wIHxFMsLMgHblWqOnbi5FjBLgUt20sqKi6R8_BS0TYVzbLL_gMkfjTjV5KqKxa4RFVSx06_rzOfnfEMQq9VCpQRz0feSIjAY0VIvEwFOUrCJXgfXox0OoaPZ-Fkxj7Mg3mv96sTtXRRZ8P8-sZ9Jf-DKpwDXNUu2X9AtrkpnIDPgC8cAWE4_hXG73VKZBX7I5bnFUzzv6xszHm5lJ4oxEZfBCA3g-3i2uT31lnErxZKqdqdUjA0GPLAjVXpx-8whXbLhKBDzdZLk6pJLq5ApG6qxboe2HI0267EnUKnK7u7s1nCPb_US7Lv2jc_46X4Wv3Q0jUZTBvcy8tqpb86teHbdkXCpzokq12RTPaKgzQFkI1d8yn1QDeaFqWxuyoKh8Ums6QzzNzvEJB2rGxoK78Yh82Ntd7zBTZ4EnpTnQ1hpGRIYhAoMW-dn3vhfzZNT2anp2lyPE_uoAMfJh1-Hx2MJ28_f2om8CTURZKbB3A7wlSu9pu62dE6O5lw9zy_ljPJA3TfzkPw2JDqIeqV60foXic75WP0s6EXbuiFFb3wDr2wohdW9MLQM96hFwZ6YUMv7OiFK4k79MItvTDQC2t6YU0v7Oj1BM1OjpM3E89W7vBySqPai6QsqRSS5EJQyXIZZ7wAy5_7fBT4GZeSgCyN81IQIkopMnAzuYgjyqQfibCgT1F_Xa3LZwiDEyx8UbAAdC6TWSBEIeHWTBQB3IuFh4i53zjNbVp7VV1lmRKX_dZCkypoUgvNIRo2zTYmr8ttDeIugGmtWS4NwVN6S9sjh3Zqzcc29XkEhlLJ9ed_vvwC3W3_ZUeoX3-7KF-CEq6zV5agvwGzkrRC
linkProvider Library Specific Holdings
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwELZaemg5lNKHoIUyh16zjRMnTo4IFS2vPYHEzXJsD43YZldsqCj_oP-6YydBCxXiwNmaie3MW-NvGPvmIVBiaeIo1jqLhM15VPkmR-QSyftIGwc4hpNJPj4Th-fZ-dJbGN9W6XNo7IAigq32yu2L0UNL3HfyMyQ5qS-JJHxEaTMvSvmSvcrKXPopBmk8uUu6eB4G23qSyNMMr3geY3PPP91DL_3PWgcXtL_GzLD5rvPkcnTdViNz-wDX8Xmne8fe9hEq7HYitc5euOY9W13CLfzA_h4ELGYylKCnF7Oruv35C3xFFxZuipG2eh4WSYLmsKhvHdD5IMCX39Q-RG4ugAJPoI2RFsAg_jBD-E25e1-fBPpg9-bzD9BpAOsbZ2E-q5sW-jk4i4_sbP_H6d446mc6RIaS4TYqEF2KGrnROkVhsKykJZtgEhlnSSUROQUspXGac-1QV2SAjC6LVGBS6Nymn9hKM2vcBgMyjzbRVmQUAQmsMq0tEmuhbUa8RL7JxPAnlekBz_3cjaniAy5qf9PK37Tqb3qTje7I5h3ix1ME5bKYqDaUWrCbi6LSJ2i3BplSvfFYqEQWpEI-kPv8DNY77PX49ORYHR9Mjr6wN7SUht45scVW2qtrt03BVFt9DdryD2uyE1I
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELZKkRAceFeUFpgD1yxx4ryOqLBqKax6aCVulmN72qhLNmpSVPoP-NeMHadqQaiHnq2Z2M68Nf6GsfcOAiUudBzFSmWRMDmPatfkiLxA8j6FiT0cw7dFvnskvnzPpm7CPrRVuhwaR6AIb6udcncGp464D-RmSHBSVxFJ-IyyZl5WxT12P3fg4e4VR7y4yrl47ufaOpLI0UyPeP7H5oZ7ugFe-o-x9h5o_oTV097HxpPT2flQz_TlX7COdzrcU_Y4xKfwcRSoZ2zNts_Zo2uohS_Y7z2PxExmEtTyeHXWDCc_wNVzobdLjJRRnV8k-emgby4t0PHAg5dfNC5Abo-Bwk6gfZEOwCT8sEL4SZl7qE4CfXB88fkL6DCAzYU10K2adoAwBad_yY7mnw93dqMw0SHSlAoPUYloU1TItVIpCo1VXRiyCDop4iypC0RO4UqlreJcWVQ1mR-tqjIVmJQqN-kGW29XrX3FgIyjSZQRGcU_AutMKYPEWiiTES-RbzIx_UipA9y5m7qxlHxCRQ03Ld1Ny3DTm2x2RdaNeB-3EVTXpUQOvtCC41QUmd5Cuz2JlAymo5dJUZICuTDu9R1Yv2MPDj7N5de9xf4We0grqW-cE9tsfTg7t28okhrqt15X_gD4LRH2
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=Iterative+algorithm+with+self-adaptive+step+size+for+approximating+the+common+solution+of+variational+inequality+and+fixed+point+problems&rft.jtitle=Optimization&rft.au=Ogwo%2C+G+N&rft.au=Alakoya%2C+T+O&rft.au=Mewomo%2C+O+T&rft.date=2023-03-04&rft.pub=Taylor+%26+Francis+LLC&rft.issn=0233-1934&rft.eissn=1029-4945&rft.volume=72&rft.issue=3&rft.spage=677&rft.epage=711&rft_id=info:doi/10.1080%2F02331934.2021.1981897&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0233-1934&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0233-1934&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0233-1934&client=summon