{"id":"https://openalex.org/W4323049087","doi":"https://doi.org/10.1007/s00500-023-07946-y","title":"The investigation of k-fuzzy metric spaces with the first contraction principle in such spaces","display_name":"The investigation of k-fuzzy metric spaces with the first contraction principle in such spaces","publication_year":2023,"publication_date":"2023-03-03","ids":{"openalex":"https://openalex.org/W4323049087","doi":"https://doi.org/10.1007/s00500-023-07946-y"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-023-07946-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-023-07946-y","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045925927","display_name":"Dhananjay Gopal","orcid":"https://orcid.org/0000-0001-8217-2778"},"institutions":[{"id":"https://openalex.org/I26285277","display_name":"Guru Ghasidas Vishwavidyalaya","ror":"https://ror.org/05bvxq496","country_code":"IN","type":"education","lineage":["https://openalex.org/I26285277"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Dhananjay Gopal","raw_affiliation_strings":["Department of Mathematics, Guru Ghasidas Vishwavidyalya Bilaspur, Bilaspur, Chhattisgarh, 495009, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guru Ghasidas Vishwavidyalya Bilaspur, Bilaspur, Chhattisgarh, 495009, India","institution_ids":["https://openalex.org/I26285277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011375789","display_name":"Wutiphol Sintunavarat","orcid":"https://orcid.org/0000-0002-0932-1332"},"institutions":[{"id":"https://openalex.org/I108108428","display_name":"Thammasat University","ror":"https://ror.org/002yp7f20","country_code":"TH","type":"education","lineage":["https://openalex.org/I108108428"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Wutiphol Sintunavarat","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Khlong Luang, Pathum Thani, 12120, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Khlong Luang, Pathum Thani, 12120, Thailand","institution_ids":["https://openalex.org/I108108428"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048111219","display_name":"A. S. Ranadive","orcid":"https://orcid.org/0000-0002-6352-9142"},"institutions":[{"id":"https://openalex.org/I26285277","display_name":"Guru Ghasidas Vishwavidyalaya","ror":"https://ror.org/05bvxq496","country_code":"IN","type":"education","lineage":["https://openalex.org/I26285277"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Abhay S. Ranadive","raw_affiliation_strings":["Department of Mathematics, Guru Ghasidas Vishwavidyalya Bilaspur, Bilaspur, Chhattisgarh, 495009, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guru Ghasidas Vishwavidyalya Bilaspur, Bilaspur, Chhattisgarh, 495009, India","institution_ids":["https://openalex.org/I26285277"]}]},{"author_position":"last","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"]},{"id":"https://openalex.org/I4405260892","display_name":"Shri Vaishnav Vidyapeeth Vishwavidyalaya, Indore","ror":"https://ror.org/04e9avw37","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405260892"]}],"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, Indore, M.P., 453331, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shri Vaishnav Institute of Science, Shri Vaishnav Vidyapeeth Vishwavidyalaya, Indore, M.P., 453331, India","institution_ids":["https://openalex.org/I138272832","https://openalex.org/I4405260892"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011375789"],"corresponding_institution_ids":["https://openalex.org/I108108428"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":4.3481,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.9520516,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"27","issue":"16","first_page":"11081","last_page":"11089"},"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":0.7703397870063782},{"id":"https://openalex.org/keywords/t-norm","display_name":"T-norm","score":0.7051534652709961},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5936870574951172},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.5834235548973083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5682543516159058},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.5633580088615417},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.5535196661949158},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.5395495295524597},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5165740251541138},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.45964479446411133},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4458999037742615},{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"Intrinsic metric","score":0.44499480724334717},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.42872896790504456},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.37528467178344727},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3532998561859131},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22274339199066162},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1775226891040802},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1416148543357849}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7703397870063782},{"id":"https://openalex.org/C2721081","wikidata":"https://www.wikidata.org/wiki/Q2383161","display_name":"T-norm","level":5,"score":0.7051534652709961},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5936870574951172},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.5834235548973083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5682543516159058},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.5633580088615417},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.5535196661949158},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.5395495295524597},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5165740251541138},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.45964479446411133},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4458999037742615},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.44499480724334717},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.42872896790504456},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.37528467178344727},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3532998561859131},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22274339199066162},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1775226891040802},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1416148543357849}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00500-023-07946-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-023-07946-y","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1780385472","https://openalex.org/W1968172834","https://openalex.org/W1987761358","https://openalex.org/W2011977682","https://openalex.org/W2038300950","https://openalex.org/W2055788103","https://openalex.org/W2067031416","https://openalex.org/W2074773690","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2255258360","https://openalex.org/W1642093767","https://openalex.org/W4387521419","https://openalex.org/W2480610033","https://openalex.org/W2119311694","https://openalex.org/W2740809164","https://openalex.org/W2610752199","https://openalex.org/W2108406645","https://openalex.org/W2886745797","https://openalex.org/W4323049087"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}