{"id":"https://openalex.org/W1974932953","doi":"https://doi.org/10.1016/s0165-0114(99)00096-2","title":"Vector-valued variational principle in fuzzy metric space and its applications","display_name":"Vector-valued variational principle in fuzzy metric space and its applications","publication_year":2001,"publication_date":"2001-04-01","ids":{"openalex":"https://openalex.org/W1974932953","doi":"https://doi.org/10.1016/s0165-0114(99)00096-2","mag":"1974932953"},"language":"en","primary_location":{"id":"doi:10.1016/s0165-0114(99)00096-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(99)00096-2","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ir.lzu.edu.cn/handle/262010/117579","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019652712","display_name":"Zhu Jiang","orcid":"https://orcid.org/0000-0002-2722-7665"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]},{"id":"https://openalex.org/I118574674","display_name":"Jiangsu Normal University","ror":"https://ror.org/051hvcm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I118574674"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiang Zhu","raw_affiliation_strings":["Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China","Department of Mathematics, Xuzhou Normal University, Xuzhou 221009, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China","institution_ids":["https://openalex.org/I76214153"]},{"raw_affiliation_string":"Department of Mathematics, Xuzhou Normal University, Xuzhou 221009, People's Republic of China","institution_ids":["https://openalex.org/I118574674"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100964535","display_name":"Chengkui Zhong","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cheng-Kui Zhong","raw_affiliation_strings":["Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China","Department of Mathematics, Lanzhou University, Lanzhou, 730000, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China","institution_ids":["https://openalex.org/I76214153"]},{"raw_affiliation_string":"Department of Mathematics, Lanzhou University, Lanzhou, 730000, People's Republic of China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036858883","display_name":"Geping Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I118574674","display_name":"Jiangsu Normal University","ror":"https://ror.org/051hvcm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I118574674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ge-Ping Wang","raw_affiliation_strings":["Department of Mathematics, Xuzhou Normal University, Xuzhou 221009, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xuzhou Normal University, Xuzhou 221009, People's Republic of China","institution_ids":["https://openalex.org/I118574674"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019652712"],"corresponding_institution_ids":["https://openalex.org/I118574674","https://openalex.org/I76214153"],"apc_list":{"value":2600,"currency":"USD","value_usd":2600},"apc_paid":null,"fwci":0.4969,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.5896677,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"119","issue":"2","first_page":"343","last_page":"354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9998000264167786,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9286999702453613,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9017999768257141,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8896839022636414},{"id":"https://openalex.org/keywords/contraction-principle","display_name":"Contraction principle","score":0.8390029668807983},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.7546083927154541},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6054632663726807},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.535331130027771},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5154715180397034},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.48645350337028503},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.44218432903289795},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4047865867614746},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3782525062561035},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35241764783859253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06330326199531555},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05538642406463623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8896839022636414},{"id":"https://openalex.org/C2775958659","wikidata":"https://www.wikidata.org/wiki/Q5165690","display_name":"Contraction principle","level":3,"score":0.8390029668807983},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.7546083927154541},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6054632663726807},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.535331130027771},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5154715180397034},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.48645350337028503},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.44218432903289795},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4047865867614746},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3782525062561035},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35241764783859253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06330326199531555},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05538642406463623},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0165-0114(99)00096-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(99)00096-2","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/117579","is_oa":true,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/117579","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ir.lzu.edu.cn/:262010/117579","is_oa":true,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/117579","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1967175421","https://openalex.org/W1968172834","https://openalex.org/W1977750299","https://openalex.org/W1980366514","https://openalex.org/W1983902189","https://openalex.org/W1995087034","https://openalex.org/W1999019219","https://openalex.org/W2008230680","https://openalex.org/W2013871828","https://openalex.org/W2018127805","https://openalex.org/W2037534711","https://openalex.org/W2038119776","https://openalex.org/W2059917091","https://openalex.org/W2085706830","https://openalex.org/W2095740654","https://openalex.org/W2139502933","https://openalex.org/W2188561910"],"related_works":["https://openalex.org/W4243687139","https://openalex.org/W2591782814","https://openalex.org/W4386037577","https://openalex.org/W4297851895","https://openalex.org/W1974932953","https://openalex.org/W4230549275","https://openalex.org/W2537611365","https://openalex.org/W4236030466","https://openalex.org/W4248946257","https://openalex.org/W75301787"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
