{"id":"https://openalex.org/W2932737122","doi":"https://doi.org/10.3390/sym11040504","title":"Caristi, Nadler and H + -Type Contractive Mappings and Their Fixed Points in \u03b8-Metric Spaces","display_name":"Caristi, Nadler and H + -Type Contractive Mappings and Their Fixed Points in \u03b8-Metric Spaces","publication_year":2019,"publication_date":"2019-04-07","ids":{"openalex":"https://openalex.org/W2932737122","doi":"https://doi.org/10.3390/sym11040504","mag":"2932737122"},"language":"en","primary_location":{"id":"doi:10.3390/sym11040504","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040504","pdf_url":"https://www.mdpi.com/2073-8994/11/4/504/pdf?version=1554630104","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/2073-8994/11/4/504/pdf?version=1554630104","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051855575","display_name":"Pradip Ramesh Patle","orcid":"https://orcid.org/0000-0002-9650-6107"},"institutions":[{"id":"https://openalex.org/I167153416","display_name":"Visvesvaraya National Institute of Technology","ror":"https://ror.org/02zrtpp84","country_code":"IN","type":"education","lineage":["https://openalex.org/I167153416"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pradip Patle","raw_affiliation_strings":["Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India","institution_ids":["https://openalex.org/I167153416"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079395394","display_name":"Jelena Vujakovi\u0107","orcid":"https://orcid.org/0000-0001-5361-7133"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jelena Vujakovi\u0107","raw_affiliation_strings":["Faculty of Sciences and Mathematics, University of Pri\u0161tina, Lole Ribara 29, Kosovska Mitrovica 38220, Serbia"],"affiliations":[{"raw_affiliation_string":"Faculty of Sciences and Mathematics, University of Pri\u0161tina, Lole Ribara 29, Kosovska Mitrovica 38220, Serbia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010838122","display_name":"Deepesh Kumar Patel","orcid":"https://orcid.org/0000-0002-5167-932X"},"institutions":[{"id":"https://openalex.org/I167153416","display_name":"Visvesvaraya National Institute of Technology","ror":"https://ror.org/02zrtpp84","country_code":"IN","type":"education","lineage":["https://openalex.org/I167153416"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Deepesh Patel","raw_affiliation_strings":["Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India","institution_ids":["https://openalex.org/I167153416"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032620709","display_name":"Stojan Radenovi\u0107","orcid":"https://orcid.org/0000-0001-8254-6688"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Stojan Radenovi\u0107","raw_affiliation_strings":["Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 71000, Vietnam","Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City 71000, Vietnam"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 71000, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City 71000, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5032620709"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3842,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55777481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"11","issue":"4","first_page":"504","last_page":"504"},"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":0.7495758533477783},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.7470532059669495},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6309452056884766},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6083725690841675},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5889964699745178},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5833544731140137},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5544426441192627},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5351444482803345},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5276785492897034},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4391290545463562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3384816646575928},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14598649740219116}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7495758533477783},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.7470532059669495},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6309452056884766},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6083725690841675},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5889964699745178},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5833544731140137},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5544426441192627},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5351444482803345},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5276785492897034},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4391290545463562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3384816646575928},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14598649740219116},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11040504","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040504","pdf_url":"https://www.mdpi.com/2073-8994/11/4/504/pdf?version=1554630104","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:d8a7c5483c41419bbff3b37d84640fea","is_oa":true,"landing_page_url":"https://doaj.org/article/d8a7c5483c41419bbff3b37d84640fea","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 4, p 504 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/4/504/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11040504","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym11040504","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040504","pdf_url":"https://www.mdpi.com/2073-8994/11/4/504/pdf?version=1554630104","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2932737122.pdf","grobid_xml":"https://content.openalex.org/works/W2932737122.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1558948865","https://openalex.org/W1981459842","https://openalex.org/W2031157165","https://openalex.org/W2044710555","https://openalex.org/W2053502445","https://openalex.org/W2067818766","https://openalex.org/W2073563789","https://openalex.org/W2084312524","https://openalex.org/W2085706830","https://openalex.org/W2116659777","https://openalex.org/W2129941846","https://openalex.org/W2478302134","https://openalex.org/W2614518851","https://openalex.org/W2883579719","https://openalex.org/W2912150934","https://openalex.org/W2963122449","https://openalex.org/W3022952999","https://openalex.org/W3164354881","https://openalex.org/W6667454692"],"related_works":["https://openalex.org/W2075445622","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"],"abstract_inverted_index":{"A":[0],"new":[1,41,86],"proper":[2],"generalization":[3],"of":[4,46,61,67,96,104,113],"metric":[5],"called":[6],"as":[7],"\u03b8":[8,47,53,75],"-metric":[9],"is":[10],"introduced":[11],"by":[12],"Khojasteh":[13],"et":[14],"al.":[15],"(Mathematical":[16],"Problems":[17],"in":[18,36,43,101],"Engineering":[19],"(2013)":[20],"Article":[21],"ID":[22],"504609).":[23],"In":[24,107],"this":[25],"paper,":[26],"first":[27],"we":[28,83,116],"prove":[29,84],"the":[30,44,73,94,102,111],"Caristi":[31],"type":[32,100],"fixed":[33,87],"point":[34,88],"theorem":[35],"an":[37],"alternative":[38],"and":[39,64,98],"comparatively":[40],"way":[42],"context":[45,103],"-metric.":[48],"We":[49],"also":[50],"investigate":[51],"two":[52,85],"-metrics":[54,76],"on":[55,77],"CB":[56,78],"(":[57,79],"X":[58,80],")":[59,81],"(family":[60],"nonempty":[62],"closed":[63],"bounded":[65],"subsets":[66],"a":[68],"set":[69],"X).":[70],"Furthermore,":[71],"using":[72],"obtained":[74],",":[82],"results":[89,95],"for":[90],"multi-functions":[91],"which":[92],"generalize":[93],"Nadler":[97],"Lim":[99],"such":[105],"spaces.":[106],"order":[108],"to":[109],"illustrate":[110],"usability":[112],"our":[114],"results,":[115],"equipped":[117],"them":[118],"with":[119],"competent":[120],"examples.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2019-04-11T00:00:00"}