{"id":"https://openalex.org/W4401419864","doi":"https://doi.org/10.3390/axioms13080536","title":"Fuzzy H-Quasi-Contraction and Fixed Point Theorems in Tripled Fuzzy Metric Spaces","display_name":"Fuzzy H-Quasi-Contraction and Fixed Point Theorems in Tripled Fuzzy Metric Spaces","publication_year":2024,"publication_date":"2024-08-07","ids":{"openalex":"https://openalex.org/W4401419864","doi":"https://doi.org/10.3390/axioms13080536"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13080536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080536","pdf_url":"https://www.mdpi.com/2075-1680/13/8/536/pdf?version=1723113954","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/8/536/pdf?version=1723113954","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101702353","display_name":"Yunpeng Zhao","orcid":"https://orcid.org/0000-0003-3018-5563"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunpeng Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","Teaching Department of Basic Course, Shanxi Vocational University of Engineering Science and Technology, Jinzhong 030619, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","institution_ids":["https://openalex.org/I2722730"]},{"raw_affiliation_string":"Teaching Department of Basic Course, Shanxi Vocational University of Engineering Science and Technology, Jinzhong 030619, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066025506","display_name":"Fei He","orcid":"https://orcid.org/0000-0001-5638-0004"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fei He","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","institution_ids":["https://openalex.org/I2722730"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111460419","display_name":"Xuan Liu","orcid":"https://orcid.org/0009-0001-8219-6400"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Liu","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","institution_ids":["https://openalex.org/I2722730"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066025506"],"corresponding_institution_ids":["https://openalex.org/I2722730"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2035648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"8","first_page":"536","last_page":"536"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.743742048740387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7367318272590637},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.659871518611908},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6403161287307739},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5710278749465942},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.562152087688446},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5469064116477966},{"id":"https://openalex.org/keywords/contraction-mapping","display_name":"Contraction mapping","score":0.5255307555198669},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44671157002449036},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40207546949386597},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.374958336353302},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32650649547576904},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2894579768180847},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22996845841407776},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11241203546524048}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.743742048740387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7367318272590637},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.659871518611908},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6403161287307739},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5710278749465942},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.562152087688446},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5469064116477966},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.5255307555198669},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44671157002449036},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40207546949386597},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.374958336353302},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32650649547576904},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2894579768180847},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22996845841407776},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11241203546524048},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13080536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080536","pdf_url":"https://www.mdpi.com/2075-1680/13/8/536/pdf?version=1723113954","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1df42a6cfef64be8988dba2880dc45fd","is_oa":true,"landing_page_url":"https://doaj.org/article/1df42a6cfef64be8988dba2880dc45fd","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":"Axioms, Vol 13, Iss 8, p 536 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13080536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080536","pdf_url":"https://www.mdpi.com/2075-1680/13/8/536/pdf?version=1723113954","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2256753543","display_name":null,"funder_award_id":"2020MS01004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4913360462","display_name":null,"funder_award_id":"2020MS01004","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G7642712001","display_name":null,"funder_award_id":"12061050","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G993330527","display_name":null,"funder_award_id":"12061050","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322868","display_name":"Natural Science Foundation of Inner Mongolia","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401419864.pdf"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1537958903","https://openalex.org/W1546035617","https://openalex.org/W1596940357","https://openalex.org/W1741223313","https://openalex.org/W1968172834","https://openalex.org/W1981992983","https://openalex.org/W1987761358","https://openalex.org/W2026244788","https://openalex.org/W2040121225","https://openalex.org/W2049226309","https://openalex.org/W2065984984","https://openalex.org/W2067031416","https://openalex.org/W2074773690","https://openalex.org/W2090240969","https://openalex.org/W2103976112","https://openalex.org/W2108028062","https://openalex.org/W2197341781","https://openalex.org/W2594987052","https://openalex.org/W2608295093","https://openalex.org/W2809576966","https://openalex.org/W2889477393","https://openalex.org/W2998857030","https://openalex.org/W3092086320","https://openalex.org/W3200665410","https://openalex.org/W4211007335","https://openalex.org/W4229078348","https://openalex.org/W4368618039","https://openalex.org/W4389782843","https://openalex.org/W4391816862","https://openalex.org/W6635703843","https://openalex.org/W6638087810","https://openalex.org/W6642368997","https://openalex.org/W6675590776","https://openalex.org/W6734931323","https://openalex.org/W6860650458"],"related_works":["https://openalex.org/W2846516035","https://openalex.org/W4249977926","https://openalex.org/W2585118952","https://openalex.org/W2012141574","https://openalex.org/W1606221119","https://openalex.org/W2354765335","https://openalex.org/W3123504591","https://openalex.org/W307954469","https://openalex.org/W2369544116","https://openalex.org/W1691643469"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,41,45,71,84,90],"concept":[3],"of":[4,44,60,73,94],"fuzzy":[5,15,50],"H-quasi-contraction":[6],"(FH-QC":[7],"for":[8,19,29,31,54,96],"short)":[9,20,30],"initiated":[10],"by":[11,99],"\u0106iri\u0107":[12],"in":[13,33,48],"tripled":[14],"metric":[16,51],"spaces":[17,52],"(T-FMSs":[18],"and":[21,62,92],"present":[22],"a":[23],"new":[24,102],"fixed":[25,74],"point":[26],"theorem":[27],"(FPT":[28],"FH-QC":[32],"complete":[34],"T-FMSs.":[35],"As":[36],"an":[37],"application,":[38],"we":[39,57,78,88],"prove":[40],"corresponding":[42,85],"results":[43],"previous":[46],"literature":[47],"setting":[49],"(FMSs":[53],"short).":[55],"Moreover,":[56],"obtain":[58],"theorems":[59],"sufficient":[61],"necessary":[63],"conditions":[64],"which":[65],"can":[66],"be":[67],"used":[68],"to":[69,82],"demonstrate":[70],"existence":[72,91],"points.":[75],"In":[76],"addition,":[77],"construct":[79],"relevant":[80],"examples":[81],"illustrate":[83],"results.":[86,103],"Finally,":[87],"show":[89],"uniqueness":[93],"solutions":[95],"integral":[97],"equations":[98],"applying":[100],"our":[101]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
