{"id":"https://openalex.org/W4401611942","doi":"https://doi.org/10.3390/axioms13080558","title":"Exploring Fixed-Point Theorems in k-Fuzzy Metric Spaces: A Comprehensive Study","display_name":"Exploring Fixed-Point Theorems in k-Fuzzy Metric Spaces: A Comprehensive Study","publication_year":2024,"publication_date":"2024-08-15","ids":{"openalex":"https://openalex.org/W4401611942","doi":"https://doi.org/10.3390/axioms13080558"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13080558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080558","pdf_url":null,"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://doi.org/10.3390/axioms13080558","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041565671","display_name":"Muhammad Nazam","orcid":"https://orcid.org/0000-0002-1274-1936"},"institutions":[{"id":"https://openalex.org/I181355716","display_name":"Allama Iqbal Open University","ror":"https://ror.org/04vympt94","country_code":"PK","type":"education","lineage":["https://openalex.org/I181355716"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Nazam","raw_affiliation_strings":["Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1274-1936","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I181355716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106549167","display_name":"Seemab Attique","orcid":"https://orcid.org/0009-0004-6287-5854"},"institutions":[{"id":"https://openalex.org/I181355716","display_name":"Allama Iqbal Open University","ror":"https://ror.org/04vympt94","country_code":"PK","type":"education","lineage":["https://openalex.org/I181355716"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Seemab Attique","raw_affiliation_strings":["Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I181355716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100758033","display_name":"Aftab Hussain","orcid":"https://orcid.org/0000-0002-7742-5993"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Aftab Hussain","raw_affiliation_strings":["Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-7742-5993","affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007351796","display_name":"Hamed Alsulami","orcid":"https://orcid.org/0000-0001-5188-2830"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hamed H. Alsulami","raw_affiliation_strings":["Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5188-2830","affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5106549167"],"corresponding_institution_ids":["https://openalex.org/I181355716"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":5.8477,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.97021154,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"13","issue":"8","first_page":"558","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9829000234603882,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6224014759063721},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5777475833892822},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5477525591850281},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5305840373039246},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.513864278793335},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4312899112701416},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4145807921886444},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32966482639312744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3275044560432434},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3217402696609497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2298576831817627},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10044613480567932},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09905686974525452},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08251368999481201},{"id":"https://openalex.org/keywords/operations-management","display_name":"Operations management","score":0.06184804439544678}],"concepts":[{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6224014759063721},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5777475833892822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5477525591850281},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5305840373039246},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.513864278793335},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4312899112701416},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4145807921886444},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32966482639312744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3275044560432434},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3217402696609497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2298576831817627},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10044613480567932},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09905686974525452},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08251368999481201},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.06184804439544678}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13080558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080558","pdf_url":null,"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:b58b5868f70a4b8ba963a10897c30480","is_oa":false,"landing_page_url":"https://doaj.org/article/b58b5868f70a4b8ba963a10897c30480","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 8, p 558 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13080558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080558","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1968172834","https://openalex.org/W1981992983","https://openalex.org/W1987761358","https://openalex.org/W2011977682","https://openalex.org/W2074773690","https://openalex.org/W3146394326","https://openalex.org/W4211007335","https://openalex.org/W4323049087","https://openalex.org/W4384205528","https://openalex.org/W4390412856","https://openalex.org/W4400057166"],"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/W2369544116","https://openalex.org/W1691643469","https://openalex.org/W2985828462"],"abstract_inverted_index":{"Recently,":[0],"k":[1,17],"-fuzzy":[2],"metric":[3,32,55,82],"spaces":[4,33],"were":[5],"introduced":[6],"by":[7],"connecting":[8],"the":[9,21,69,77,86,118],"degree":[10],"of":[11,13,26,71,74,88,120,122],"nearness":[12],"two":[14],"points":[15,73],"with":[16,35,91],"parameters":[18],"(t1,t2,t3,\u22ef,tk)":[19],"and":[20,99],"authors":[22],"presented":[23,41],"an":[24,109],"analogue":[25],"Grabiec\u2019s":[27],"fixed-point":[28,63,97,100,114],"result":[29,52,115],"in":[30,53,80],"k-fuzzy":[31,54,81,104],"along":[34],"other":[36],"necessary":[37,66],"notions.":[38],"The":[39],"results":[40,64],"only":[42],"addressed":[43],"continuous":[44],"mappings.":[45],"For":[46],"discontinuous":[47],"mappings,":[48],"there":[49],"is":[50],"no":[51],"spaces.":[56,83],"In":[57],"this":[58],"paper,":[59],"we":[60,111],"obtain":[61],"some":[62],"stating":[65],"conditions":[67],"for":[68,102],"existence":[70,119],"fixed":[72],"mappings":[75],"eliminating":[76],"continuity":[78],"requirement":[79],"We":[84,93],"illustrate":[85],"hypothesis":[87],"our":[89],"findings":[90],"examples.":[92],"provide":[94],"a":[95,113],"common":[96],"theorem":[98],"theorems":[101],"single-valued":[103],"Kannan":[105],"type":[106],"contractions.":[107],"As":[108],"application,":[110],"use":[112],"to":[116],"ensure":[117],"solution":[121],"fractional":[123],"differential":[124],"equations.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}