{"id":"https://openalex.org/W1980574866","doi":"https://doi.org/10.1155/2012/235474","title":"Viscosity Approximations by the Shrinking Projection Method of Quasi\u2010Nonexpansive Mappings for Generalized Equilibrium Problems","display_name":"Viscosity Approximations by the Shrinking Projection Method of Quasi\u2010Nonexpansive Mappings for Generalized Equilibrium Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1980574866","doi":"https://doi.org/10.1155/2012/235474","mag":"1980574866"},"language":"en","primary_location":{"id":"doi:10.1155/2012/235474","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/235474","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/235474.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/235474.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071816548","display_name":"Rabian Wangkeeree","orcid":"https://orcid.org/0000-0002-5715-3804"},"institutions":[{"id":"https://openalex.org/I66200439","display_name":"Naresuan University","ror":"https://ror.org/03e2qe334","country_code":"TH","type":"education","lineage":["https://openalex.org/I66200439"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Rabian Wangkeeree","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand","Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand","institution_ids":["https://openalex.org/I66200439"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand#TAB#","institution_ids":["https://openalex.org/I66200439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042690366","display_name":"Nimit Nimana","orcid":"https://orcid.org/0000-0003-1640-8919"},"institutions":[{"id":"https://openalex.org/I66200439","display_name":"Naresuan University","ror":"https://ror.org/03e2qe334","country_code":"TH","type":"education","lineage":["https://openalex.org/I66200439"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Nimit Nimana","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand","Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand","institution_ids":["https://openalex.org/I66200439"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand#TAB#","institution_ids":["https://openalex.org/I66200439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071816548"],"corresponding_institution_ids":["https://openalex.org/I66200439"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3461,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5982106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7646471261978149},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.7446735501289368},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6965869665145874},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.6822384595870972},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5870165228843689},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5125668048858643},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4962039589881897},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4632946252822876},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45295771956443787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43264102935791016},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2645585536956787},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.21849429607391357},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1590428352355957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11490213871002197},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0865665078163147},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08369964361190796}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7646471261978149},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7446735501289368},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6965869665145874},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.6822384595870972},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5870165228843689},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5125668048858643},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4962039589881897},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4632946252822876},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45295771956443787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43264102935791016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2645585536956787},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.21849429607391357},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1590428352355957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11490213871002197},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0865665078163147},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08369964361190796},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/235474","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/235474","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/235474.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1357177646","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1357177646","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:235474","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/235474.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:f2e41c068a3f44f788930432810204cb","is_oa":true,"landing_page_url":"https://doaj.org/article/f2e41c068a3f44f788930432810204cb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/235474","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/235474","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/235474.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323020","display_name":"Naresuan University","ror":"https://ror.org/03e2qe334"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1980574866.pdf","grobid_xml":"https://content.openalex.org/works/W1980574866.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W154593720","https://openalex.org/W901968330","https://openalex.org/W1458771408","https://openalex.org/W1487976166","https://openalex.org/W1579117477","https://openalex.org/W1976746644","https://openalex.org/W1977111935","https://openalex.org/W1977798603","https://openalex.org/W1980232119","https://openalex.org/W1986983198","https://openalex.org/W2003282727","https://openalex.org/W2009587401","https://openalex.org/W2027068897","https://openalex.org/W2033943991","https://openalex.org/W2044351385","https://openalex.org/W2053009427","https://openalex.org/W2056838549","https://openalex.org/W2063792642","https://openalex.org/W2069435104","https://openalex.org/W2070694134","https://openalex.org/W2078742969","https://openalex.org/W2116659777","https://openalex.org/W2266418310","https://openalex.org/W2753109682","https://openalex.org/W2801143022","https://openalex.org/W6692973537"],"related_works":["https://openalex.org/W4323058680","https://openalex.org/W2391553691","https://openalex.org/W2531545003","https://openalex.org/W2393270639","https://openalex.org/W3103135560","https://openalex.org/W774881382","https://openalex.org/W2617963432","https://openalex.org/W2033390858","https://openalex.org/W2899022965","https://openalex.org/W2392770728"],"abstract_inverted_index":{"We":[0],"introduce":[1],"viscosity":[2,46],"approximations":[3],"by":[4,11],"using":[5],"the":[6,22,27,32,45,56,61,66,72],"shrinking":[7,47],"projection":[8,48],"method":[9,49],"established":[10],"Takahashi,":[12],"Takeuchi,":[13],"and":[14,31,65],"Kubota,":[15],"for":[16,50],"finding":[17,51],"a":[18,38,52],"common":[19,53],"element":[20,54],"of":[21,24,26,34,37,55,58,60,68,71],"set":[23,33,57,67],"solutions":[25,59],"generalized":[28,62],"equilibrium":[29,63],"problem":[30,64],"fixed":[35,69],"points":[36,70],"quasi\u2010nonexpansive":[39],"mapping.":[40],"Furthermore,":[41],"we":[42],"also":[43],"consider":[44],"super":[73],"hybrid":[74],"mappings":[75],"in":[76],"Hilbert":[77],"spaces.":[78]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}