{"id":"https://openalex.org/W2997569543","doi":"https://doi.org/10.1109/access.2019.2963024","title":"The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces","display_name":"The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces","publication_year":2019,"publication_date":"2019-12-31","ids":{"openalex":"https://openalex.org/W2997569543","doi":"https://doi.org/10.1109/access.2019.2963024","mag":"2997569543"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2963024","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2963024","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08945216.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08945216.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032159193","display_name":"Xingchao Bian","orcid":"https://orcid.org/0000-0002-7580-5992"},"institutions":[{"id":"https://openalex.org/I4210089639","display_name":"Suihua University","ror":"https://ror.org/009qwp447","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210089639"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xingchao Bian","raw_affiliation_strings":["College of Information Engineering, Suihua University, Suihua, China"],"affiliations":[{"raw_affiliation_string":"College of Information Engineering, Suihua University, Suihua, China","institution_ids":["https://openalex.org/I4210089639"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057483905","display_name":"Sundus Shahzeen","orcid":"https://orcid.org/0000-0002-8087-3228"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sundus Shahzeen","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I142204992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054055136","display_name":"Mujahid Abbas","orcid":"https://orcid.org/0000-0001-5528-1207"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK","TW"],"is_corresponding":false,"raw_author_name":"Mujahid Abbas","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore, Pakistan","Department of Medical Research, China Medical University, Taichung, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University, Taichung, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102981415","display_name":"Maqbool Ahmad","orcid":"https://orcid.org/0000-0002-8706-3711"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. Saeed Ahmad","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074718815","display_name":"Binli Zhang","orcid":"https://orcid.org/0000-0002-6627-1343"},"institutions":[{"id":"https://openalex.org/I4210089639","display_name":"Suihua University","ror":"https://ror.org/009qwp447","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210089639"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binli Zhang","raw_affiliation_strings":["Institute of Economic Management, Suihua University, Suihua, China"],"affiliations":[{"raw_affiliation_string":"Institute of Economic Management, Suihua University, Suihua, China","institution_ids":["https://openalex.org/I4210089639"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032159193"],"corresponding_institution_ids":["https://openalex.org/I4210089639"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21077545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"first_page":"7423","last_page":"7434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9980999827384949,"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":0.9932000041007996,"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/convergence","display_name":"Convergence (economics)","score":0.7418718338012695},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.7004029750823975},{"id":"https://openalex.org/keywords/iterative-and-incremental-development","display_name":"Iterative and incremental development","score":0.6364336609840393},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5839928984642029},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.532382607460022},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5254127979278564},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.5047479867935181},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5005278587341309},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4337432384490967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.422821581363678},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.337831974029541},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3299613893032074},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1616724133491516}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7418718338012695},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.7004029750823975},{"id":"https://openalex.org/C143587482","wikidata":"https://www.wikidata.org/wiki/Q1543216","display_name":"Iterative and incremental development","level":2,"score":0.6364336609840393},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5839928984642029},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.532382607460022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5254127979278564},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.5047479867935181},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5005278587341309},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4337432384490967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.422821581363678},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.337831974029541},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3299613893032074},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1616724133491516},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2963024","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2963024","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08945216.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:01d74f89938846feb872d418fa9da583","is_oa":true,"landing_page_url":"https://doaj.org/article/01d74f89938846feb872d418fa9da583","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 7423-7434 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2963024","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2963024","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08945216.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2997569543.pdf","grobid_xml":"https://content.openalex.org/works/W2997569543.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W27836280","https://openalex.org/W1586096349","https://openalex.org/W1748523426","https://openalex.org/W1950518118","https://openalex.org/W1966233677","https://openalex.org/W1968699683","https://openalex.org/W1976650207","https://openalex.org/W1995430313","https://openalex.org/W2002782088","https://openalex.org/W2008145369","https://openalex.org/W2033943991","https://openalex.org/W2037156580","https://openalex.org/W2046292142","https://openalex.org/W2064507512","https://openalex.org/W2067902429","https://openalex.org/W2070694134","https://openalex.org/W2084498349","https://openalex.org/W2122759586","https://openalex.org/W2134086356","https://openalex.org/W2136496202","https://openalex.org/W2140422129","https://openalex.org/W2155802942","https://openalex.org/W2167400582","https://openalex.org/W2275378654","https://openalex.org/W2343316444","https://openalex.org/W2469615143","https://openalex.org/W2585113272","https://openalex.org/W2596230329","https://openalex.org/W2769870014","https://openalex.org/W2795836422","https://openalex.org/W2910668859","https://openalex.org/W2947027196","https://openalex.org/W2947234601","https://openalex.org/W2960146582","https://openalex.org/W2961238587","https://openalex.org/W2967345134","https://openalex.org/W2978427269","https://openalex.org/W3207212243","https://openalex.org/W4231777091","https://openalex.org/W4249666993","https://openalex.org/W6750049348","https://openalex.org/W6765127804"],"related_works":["https://openalex.org/W3012343072","https://openalex.org/W2361653725","https://openalex.org/W2498640783","https://openalex.org/W2022562732","https://openalex.org/W1495035728","https://openalex.org/W3094835310","https://openalex.org/W2034475059","https://openalex.org/W2120731657","https://openalex.org/W2026748623","https://openalex.org/W2362473129"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,18,26,36,52,66],"this":[3],"paper":[4],"is":[5,47],"to":[6],"investigate":[7],"implicit":[8],"viscosity":[9],"iterative":[10],"algorithm":[11,28,46],"for":[12],"nonexpansive":[13],"mappings":[14],"in":[15,56],"the":[16,34,44],"framework":[17],"CAT(0)":[19],"spaces.":[20],"We":[21,40],"prove":[22],"strong":[23],"convergence":[24],"theorems":[25],"such":[27],"under":[29],"some":[30,63],"suitable":[31],"assumptions":[32],"on":[33],"sequences":[35],"parameters":[37],"involved":[38],"therein.":[39],"also":[41],"proved":[42],"that":[43],"presented":[45],"faster":[48],"than":[49],"a":[50],"number":[51],"existing":[53],"iteration":[54],"processes":[55],"literature.":[57],"Our":[58],"results":[59,65],"extend":[60],"and":[61,76],"improve":[62],"recent":[64],"Ahmad":[67],"et":[68],"al.[J.":[69],"Appl.":[70],"Math.":[71],"Informatics":[72],"35":[73],"(5-6)(2017),":[74],"423-438]":[75],"others.":[77]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}