{"id":"https://openalex.org/W4386879260","doi":"https://doi.org/10.3390/sym15091797","title":"Some Fixed Point Theorems for \u03b1-Admissible Mappings in Complex-Valued Fuzzy Metric Spaces","display_name":"Some Fixed Point Theorems for \u03b1-Admissible Mappings in Complex-Valued Fuzzy Metric Spaces","publication_year":2023,"publication_date":"2023-09-20","ids":{"openalex":"https://openalex.org/W4386879260","doi":"https://doi.org/10.3390/sym15091797"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091797","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091797","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1797/pdf?version=1695220787","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/2073-8994/15/9/1797/pdf?version=1695220787","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091324798","display_name":"Satish Shukla","orcid":"https://orcid.org/0000-0002-5158-3504"},"institutions":[{"id":"https://openalex.org/I138272832","display_name":"Devi Ahilya Vishwavidyalaya","ror":"https://ror.org/05c2p1f98","country_code":"IN","type":"education","lineage":["https://openalex.org/I138272832"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Satish Shukla","raw_affiliation_strings":["Department of Mathematics, Shri Vaishnav Institute of Science, Shri Vaishnav Vidyapeeth Vishwavidyalaya, Gram Baroli Sanwer Road, Indore 453331, India"],"raw_orcid":"https://orcid.org/0000-0002-5158-3504","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shri Vaishnav Institute of Science, Shri Vaishnav Vidyapeeth Vishwavidyalaya, Gram Baroli Sanwer Road, Indore 453331, India","institution_ids":["https://openalex.org/I138272832"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073678080","display_name":"Shweta Rai","orcid":"https://orcid.org/0000-0002-4624-3521"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shweta Rai","raw_affiliation_strings":["Department of Mathematics, Acropolis Institute of Technology & Research, Indore 453771, India"],"raw_orcid":"https://orcid.org/0000-0002-4624-3521","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Acropolis Institute of Technology & Research, Indore 453771, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074290395","display_name":"Rahul Shukla","orcid":"https://orcid.org/0000-0002-9835-0935"},"institutions":[{"id":"https://openalex.org/I92579986","display_name":"Walter Sisulu University","ror":"https://ror.org/02svzjn28","country_code":"ZA","type":"education","lineage":["https://openalex.org/I92579986"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Rahul Shukla","raw_affiliation_strings":["Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha 5117, South Africa"],"raw_orcid":"https://orcid.org/0000-0002-9835-0935","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha 5117, South Africa","institution_ids":["https://openalex.org/I92579986"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074290395"],"corresponding_institution_ids":["https://openalex.org/I92579986"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.4175,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.89186878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"15","issue":"9","first_page":"1797","last_page":"1797"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7398273944854736},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6501532196998596},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.582412838935852},{"id":"https://openalex.org/keywords/product-metric","display_name":"Product metric","score":0.5350182056427002},{"id":"https://openalex.org/keywords/t-norm","display_name":"T-norm","score":0.48440128564834595},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4684973359107971},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.466930091381073},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46381279826164246},{"id":"https://openalex.org/keywords/metric-map","display_name":"Metric map","score":0.4377526044845581},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4296375811100006},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.424392431974411},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42409658432006836},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.41613495349884033},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3586125373840332},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.2795383930206299},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.26859450340270996},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2376415729522705},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17227652668952942},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08015450835227966},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04230883717536926}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7398273944854736},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6501532196998596},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.582412838935852},{"id":"https://openalex.org/C154497576","wikidata":"https://www.wikidata.org/wiki/Q7247777","display_name":"Product metric","level":3,"score":0.5350182056427002},{"id":"https://openalex.org/C2721081","wikidata":"https://www.wikidata.org/wiki/Q2383161","display_name":"T-norm","level":5,"score":0.48440128564834595},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4684973359107971},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.466930091381073},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46381279826164246},{"id":"https://openalex.org/C145084290","wikidata":"https://www.wikidata.org/wiki/Q2713824","display_name":"Metric map","level":4,"score":0.4377526044845581},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4296375811100006},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.424392431974411},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42409658432006836},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.41613495349884033},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3586125373840332},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.2795383930206299},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.26859450340270996},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2376415729522705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17227652668952942},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08015450835227966},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04230883717536926},{"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:10.3390/sym15091797","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091797","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1797/pdf?version=1695220787","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:0653a86231264278be9c49df43156335","is_oa":false,"landing_page_url":"https://doaj.org/article/0653a86231264278be9c49df43156335","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":"Symmetry, Vol 15, Iss 9, p 1797 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15091797","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091797","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1797/pdf?version=1695220787","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":[],"awards":[{"id":"https://openalex.org/G989253599","display_name":null,"funder_award_id":"TAR/2022/000131","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386879260.pdf","grobid_xml":"https://content.openalex.org/works/W4386879260.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1596940357","https://openalex.org/W1968172834","https://openalex.org/W1987761358","https://openalex.org/W1997420781","https://openalex.org/W2011328341","https://openalex.org/W2015422857","https://openalex.org/W2061043245","https://openalex.org/W2068416074","https://openalex.org/W2074773690","https://openalex.org/W2093539220","https://openalex.org/W2122335161","https://openalex.org/W2131174231","https://openalex.org/W2132810216","https://openalex.org/W2145364632","https://openalex.org/W2168203105","https://openalex.org/W2323245002","https://openalex.org/W2345697831","https://openalex.org/W2517033404","https://openalex.org/W2793405200","https://openalex.org/W2793986259","https://openalex.org/W2809315816","https://openalex.org/W2923809396","https://openalex.org/W2964023683","https://openalex.org/W3094906613","https://openalex.org/W3165213760","https://openalex.org/W3171283943","https://openalex.org/W4211007335","https://openalex.org/W4378905953","https://openalex.org/W4386420495","https://openalex.org/W6635703843","https://openalex.org/W6653255691","https://openalex.org/W6795952724"],"related_works":["https://openalex.org/W2610752199","https://openalex.org/W2029705245","https://openalex.org/W2740809164","https://openalex.org/W2007002740","https://openalex.org/W2241443256","https://openalex.org/W4210552450","https://openalex.org/W2226253657","https://openalex.org/W2802428694","https://openalex.org/W112388006","https://openalex.org/W2348911274"],"abstract_inverted_index":{"This":[0],"paper":[1,41],"discusses":[2],"some":[3],"properties":[4],"of":[5,18,39],"complex-valued":[6,19,53],"fuzzy":[7,20,50,54],"metric":[8,21,55],"spaces":[9],"and":[10,44,52,63,69],"introduces":[11],"the":[12,16,65],"\u03b1-admissible":[13],"mappings":[14,29],"in":[15],"setting":[17],"spaces.":[22,56],"We":[23],"establish":[24],"fixed":[25],"point":[26],"theorems":[27],"for":[28],"satisfying":[30],"symmetric":[31],"contractive":[32],"conditions":[33],"with":[34],"control":[35],"functions.":[36],"The":[37],"results":[38,47],"this":[40],"generalize,":[42],"extend,":[43],"improve":[45],"several":[46],"from":[48],"metric,":[49,51],"Several":[57],"examples":[58],"are":[59],"presented":[60],"that":[61],"verify":[62],"illustrate":[64],"new":[66],"concepts,":[67],"claims,":[68],"results.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}