{"id":"https://openalex.org/W3214821229","doi":"https://doi.org/10.3390/sym13122250","title":"A Modified Tseng\u2019s Method for Solving the Modified Variational Inclusion Problems and Its Applications","display_name":"A Modified Tseng\u2019s Method for Solving the Modified Variational Inclusion Problems and Its Applications","publication_year":2021,"publication_date":"2021-11-25","ids":{"openalex":"https://openalex.org/W3214821229","doi":"https://doi.org/10.3390/sym13122250","mag":"3214821229"},"language":"en","primary_location":{"id":"doi:10.3390/sym13122250","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122250","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2250/pdf?version=1637888026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/12/2250/pdf?version=1637888026","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016172315","display_name":"Thidaporn Seangwattana","orcid":"https://orcid.org/0000-0002-1240-1181"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Thidaporn Seangwattana","raw_affiliation_strings":["Faculty of Science Energy and Environment, King Mongkut\u2019s University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong 21120, Thailand","Faculty of Science Energy and Environment, King Mongkut's University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong 21120, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-1240-1181","affiliations":[{"raw_affiliation_string":"Faculty of Science Energy and Environment, King Mongkut\u2019s University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong 21120, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Faculty of Science Energy and Environment, King Mongkut's University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong 21120, Thailand","institution_ids":["https://openalex.org/I82828225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024901697","display_name":"Kamonrat Sombut","orcid":"https://orcid.org/0000-0002-8775-4790"},"institutions":[{"id":"https://openalex.org/I10245363","display_name":"Rajamangala University of Technology","ror":"https://ror.org/051qqcg15","country_code":"TH","type":"education","lineage":["https://openalex.org/I10245363"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Kamonrat Sombut","raw_affiliation_strings":["Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-8775-4790","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand","institution_ids":["https://openalex.org/I10245363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059391955","display_name":"Areerat Arunchai","orcid":"https://orcid.org/0000-0001-9569-4057"},"institutions":[{"id":"https://openalex.org/I4210138454","display_name":"Nakhon Sawan Rajabhat University","ror":"https://ror.org/0408gh695","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210138454"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Areerat Arunchai","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand"],"raw_orcid":"https://orcid.org/0000-0001-9569-4057","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand","institution_ids":["https://openalex.org/I4210138454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011924128","display_name":"Kanokwan S\u0131tth\u0131thakerngk\u0131et","orcid":"https://orcid.org/0000-0002-8496-7803"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Kanokwan Sitthithakerngkiet","raw_affiliation_strings":["Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10587, Thailand","Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10587, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-8496-7803","affiliations":[{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10587, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10587, Thailand","institution_ids":["https://openalex.org/I82828225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011924128"],"corresponding_institution_ids":["https://openalex.org/I82828225"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.6594,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73506768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"13","issue":"12","first_page":"2250","last_page":"2250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.995199978351593,"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":0.995199978351593,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6861160397529602},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5583822727203369},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5402474403381348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5326411724090576},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.4795805513858795},{"id":"https://openalex.org/keywords/inertial-frame-of-reference","display_name":"Inertial frame of reference","score":0.4691183865070343},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.44678935408592224},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4242510199546814},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39653339982032776},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3789029121398926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3738490343093872},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.24179735779762268},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16900473833084106},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.053185105323791504}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6861160397529602},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5583822727203369},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5402474403381348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5326411724090576},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.4795805513858795},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.4691183865070343},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.44678935408592224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4242510199546814},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39653339982032776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3789029121398926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3738490343093872},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.24179735779762268},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16900473833084106},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.053185105323791504},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13122250","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122250","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2250/pdf?version=1637888026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5c6db1d89f99400c9a91650601857287","is_oa":true,"landing_page_url":"https://doaj.org/article/5c6db1d89f99400c9a91650601857287","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 12, p 2250 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/12/2250/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13122250","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13122250","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122250","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2250/pdf?version=1637888026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320324344","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97"},{"id":"https://openalex.org/F4320326420","display_name":"Rajamangala University of Technology Thanyaburi","ror":"https://ror.org/051qqcg15"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3214821229.pdf","grobid_xml":"https://content.openalex.org/works/W3214821229.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W199410564","https://openalex.org/W1980223035","https://openalex.org/W1986210113","https://openalex.org/W1987427505","https://openalex.org/W1998576973","https://openalex.org/W2019569173","https://openalex.org/W2048408528","https://openalex.org/W2053487511","https://openalex.org/W2055467852","https://openalex.org/W2058532290","https://openalex.org/W2063357812","https://openalex.org/W2069356606","https://openalex.org/W2091512449","https://openalex.org/W2100503136","https://openalex.org/W2603940458","https://openalex.org/W2788242395","https://openalex.org/W2800783024","https://openalex.org/W2898652318","https://openalex.org/W2943265018","https://openalex.org/W2969945254","https://openalex.org/W2993347174","https://openalex.org/W3009326592","https://openalex.org/W3010717203","https://openalex.org/W3011154760","https://openalex.org/W3016916345","https://openalex.org/W3025080527","https://openalex.org/W3100826675","https://openalex.org/W3103376690","https://openalex.org/W3110857087","https://openalex.org/W3119425556","https://openalex.org/W3178176990","https://openalex.org/W3197604085","https://openalex.org/W4200153169","https://openalex.org/W4229650096","https://openalex.org/W6662321842","https://openalex.org/W6766816269","https://openalex.org/W6774916324","https://openalex.org/W6801340264"],"related_works":["https://openalex.org/W3125070615","https://openalex.org/W2357322570","https://openalex.org/W2997591215","https://openalex.org/W2227541280","https://openalex.org/W4389558692","https://openalex.org/W2883846442","https://openalex.org/W2029783634","https://openalex.org/W2974904990","https://openalex.org/W2365681766","https://openalex.org/W2393963626"],"abstract_inverted_index":{"The":[0],"goal":[1],"of":[2,34,80],"this":[3,22],"study":[4],"was":[5],"to":[6,41,75,112],"show":[7,107],"how":[8],"a":[9,26,59,96],"modified":[10,27],"variational":[11],"inclusion":[12],"problem":[13],"can":[14],"be":[15],"solved":[16],"based":[17],"on":[18],"Tseng\u2019s":[19,28,46],"method.":[20,37,83],"In":[21],"study,":[23],"we":[24,106],"propose":[25],"method":[29,39,47,87],"and":[30,52,66,70,99],"increase":[31],"the":[32,35,43,53,77,81,85,101,108],"reliability":[33],"proposed":[36,82,86],"This":[38],"is":[40,88],"modify":[42],"relaxed":[44],"inertial":[45],"by":[48],"using":[49],"certain":[50],"conditions":[51],"parallel":[54],"technique.":[55],"We":[56],"also":[57],"prove":[58],"weak":[60],"convergence":[61,78],"theorem":[62],"under":[63],"appropriate":[64],"assumptions":[65],"some":[67],"symmetry":[68],"properties":[69],"then":[71],"provide":[72],"numerical":[73],"experiments":[74],"demonstrate":[76],"behavior":[79],"Moreover,":[84],"used":[89],"for":[90],"image":[91,98,114],"restoration":[92],"technology,":[93],"which":[94],"takes":[95],"corrupt/noisy":[97],"estimates":[100],"clean,":[102],"original":[103],"image.":[104],"Finally,":[105],"signal-to-noise":[109],"ratio":[110],"(SNR)":[111],"guarantee":[113],"quality.":[115]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}