{"id":"https://openalex.org/W4381681284","doi":"https://doi.org/10.3390/axioms12070616","title":"A Fixed Point Theorem for Generalized \u0106iri\u0107-Type Contraction in Kaleva\u2013Seikkala\u2019s Type Fuzzy b-Metric Spaces","display_name":"A Fixed Point Theorem for Generalized \u0106iri\u0107-Type Contraction in Kaleva\u2013Seikkala\u2019s Type Fuzzy b-Metric Spaces","publication_year":2023,"publication_date":"2023-06-21","ids":{"openalex":"https://openalex.org/W4381681284","doi":"https://doi.org/10.3390/axioms12070616"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12070616","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070616","pdf_url":"https://www.mdpi.com/2075-1680/12/7/616/pdf?version=1687351879","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/2075-1680/12/7/616/pdf?version=1687351879","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091054448","display_name":"Jiaojiao Wu","orcid":"https://orcid.org/0009-0007-4404-8304"},"institutions":[{"id":"https://openalex.org/I228616957","display_name":"Inner Mongolia University of Finance and Economics","ror":"https://ror.org/02311bm93","country_code":"CN","type":"education","lineage":["https://openalex.org/I228616957"]},{"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":"Jiaojiao Wu","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","School of Statistics and Mathematics, Inner Mongolia University of Financial and Economic, Hohhot 010070, China"],"raw_orcid":"https://orcid.org/0009-0007-4404-8304","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","institution_ids":["https://openalex.org/I2722730"]},{"raw_affiliation_string":"School of Statistics and Mathematics, Inner Mongolia University of Financial and Economic, Hohhot 010070, China","institution_ids":["https://openalex.org/I228616957"]}]},{"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":"https://orcid.org/0000-0001-5638-0004","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/A5013800569","display_name":"Shu-fang Li","orcid":"https://orcid.org/0000-0003-4392-5735"},"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":"Shufang Li","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"],"raw_orcid":"https://orcid.org/0000-0003-4392-5735","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":2,"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":1.0039,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72118322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"12","issue":"7","first_page":"616","last_page":"616"},"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":0.7937224507331848},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.7433043122291565},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6764216423034668},{"id":"https://openalex.org/keywords/contraction-mapping","display_name":"Contraction mapping","score":0.6679208278656006},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6398845911026001},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.6215741038322449},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5565405488014221},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.48827528953552246},{"id":"https://openalex.org/keywords/picard\u2013lindel\u00f6f-theorem","display_name":"Picard\u2013Lindel\u00f6f theorem","score":0.4693000912666321},{"id":"https://openalex.org/keywords/complete-metric-space","display_name":"Complete metric space","score":0.4652792811393738},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45549046993255615},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4150354564189911},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4133557379245758},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.383340984582901},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35947638750076294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11904630064964294}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7937224507331848},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.7433043122291565},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6764216423034668},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.6679208278656006},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6398845911026001},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.6215741038322449},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5565405488014221},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.48827528953552246},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.4693000912666321},{"id":"https://openalex.org/C93361540","wikidata":"https://www.wikidata.org/wiki/Q848569","display_name":"Complete metric space","level":3,"score":0.4652792811393738},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45549046993255615},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4150354564189911},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4133557379245758},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.383340984582901},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35947638750076294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11904630064964294},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12070616","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070616","pdf_url":"https://www.mdpi.com/2075-1680/12/7/616/pdf?version=1687351879","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:df4703795c374247b4866247dc948e00","is_oa":true,"landing_page_url":"https://doaj.org/article/df4703795c374247b4866247dc948e00","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 12, Iss 7, p 616 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/7/616/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12070616","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 7; Pages: 616","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12070616","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070616","pdf_url":"https://www.mdpi.com/2075-1680/12/7/616/pdf?version=1687351879","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/G2248973526","display_name":null,"funder_award_id":"NJZY22324","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"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/G6620130211","display_name":null,"funder_award_id":"NJZY22324","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G7631334135","display_name":null,"funder_award_id":"NJZY22324","funder_id":"https://openalex.org/F4320327830","funder_display_name":"Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region"},{"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},{"id":"https://openalex.org/F4320327830","display_name":"Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4381681284.pdf","grobid_xml":"https://content.openalex.org/works/W4381681284.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W72134831","https://openalex.org/W1458771408","https://openalex.org/W1867813010","https://openalex.org/W2008230680","https://openalex.org/W2012795412","https://openalex.org/W2032966383","https://openalex.org/W2065984984","https://openalex.org/W2066797282","https://openalex.org/W2069069851","https://openalex.org/W2112786166","https://openalex.org/W2805623295","https://openalex.org/W2985490497","https://openalex.org/W4252219081","https://openalex.org/W4308105634","https://openalex.org/W4309440873","https://openalex.org/W4311035432","https://openalex.org/W4319962498","https://openalex.org/W6602953246"],"related_works":["https://openalex.org/W2302784006","https://openalex.org/W4284888934","https://openalex.org/W4384932940","https://openalex.org/W329565398","https://openalex.org/W3087579690","https://openalex.org/W3103699964","https://openalex.org/W2793131360","https://openalex.org/W138666971","https://openalex.org/W4287665255","https://openalex.org/W75301787"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,45],"state":[4],"and":[5,25,49],"establish":[6],"a":[7],"new":[8],"fixed":[9],"point":[10],"theorem":[11],"for":[12],"generalized":[13],"\u0106iri\u0107-type":[14],"contraction":[15],"in":[16,30,58],"Kaleva-Seikkala\u2019s":[17],"type":[18,60],"fuzzy":[19,61],"b-metric":[20,62],"space.":[21,63],"Our":[22],"results":[23,29],"improve":[24],"extend":[26],"some":[27],"well-known":[28],"the":[31,47],"literature.":[32],"Some":[33],"examples":[34],"are":[35],"given":[36],"to":[37,53],"support":[38],"our":[39],"result.":[40],"Finally,":[41],"as":[42],"an":[43],"application,":[44],"show":[46],"existence":[48],"uniqueness":[50],"of":[51],"solution":[52],"Volterra":[54],"integral":[55],"equation":[56],"formulated":[57],"Kaleva\u2013Seikkala\u2019s":[59]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-06-23T00:00:00"}