{"id":"https://openalex.org/W2051501037","doi":"https://doi.org/10.1007/s10107-009-0316-3","title":"Towards variational analysis in metric spaces: metric regularity and fixed points","display_name":"Towards variational analysis in metric spaces: metric regularity and fixed points","publication_year":2009,"publication_date":"2009-11-10","ids":{"openalex":"https://openalex.org/W2051501037","doi":"https://doi.org/10.1007/s10107-009-0316-3","mag":"2051501037"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-009-0316-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-009-0316-3","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5016871466","display_name":"A. D. Ioffe","orcid":"https://orcid.org/0000-0001-5643-5706"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"A. D. Ioffe","raw_affiliation_strings":["Department of Mathematics, Technion, Haifa, 32000, Israel","Technion, Department of Mathematics, 32000, Haifa, Israel#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technion, Haifa, 32000, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Technion, Department of Mathematics, 32000, Haifa, Israel#TAB#","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016871466"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":6.9411,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.9793122,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"123","issue":"1","first_page":"241","last_page":"252"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9620000123977661,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8993417024612427},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6940771341323853},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6004762053489685},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.5880743265151978},{"id":"https://openalex.org/keywords/contraction-mapping","display_name":"Contraction mapping","score":0.5671391487121582},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5586308240890503},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5471320748329163},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.5421297550201416},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5259965658187866},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48601633310317993},{"id":"https://openalex.org/keywords/contraction-principle","display_name":"Contraction principle","score":0.45419245958328247},{"id":"https://openalex.org/keywords/complete-metric-space","display_name":"Complete metric space","score":0.45254090428352356},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.43673160672187805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4348224401473999},{"id":"https://openalex.org/keywords/metric-map","display_name":"Metric map","score":0.41223573684692383},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3750007748603821}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8993417024612427},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6940771341323853},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6004762053489685},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.5880743265151978},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.5671391487121582},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5586308240890503},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5471320748329163},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.5421297550201416},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5259965658187866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48601633310317993},{"id":"https://openalex.org/C2775958659","wikidata":"https://www.wikidata.org/wiki/Q5165690","display_name":"Contraction principle","level":3,"score":0.45419245958328247},{"id":"https://openalex.org/C93361540","wikidata":"https://www.wikidata.org/wiki/Q848569","display_name":"Complete metric space","level":3,"score":0.45254090428352356},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.43673160672187805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4348224401473999},{"id":"https://openalex.org/C145084290","wikidata":"https://www.wikidata.org/wiki/Q2713824","display_name":"Metric map","level":4,"score":0.41223573684692383},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3750007748603821}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-009-0316-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-009-0316-3","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1493492050","https://openalex.org/W1632219083","https://openalex.org/W1991203806","https://openalex.org/W1993647205","https://openalex.org/W2002103095","https://openalex.org/W2011988520","https://openalex.org/W2038301844","https://openalex.org/W2046370168","https://openalex.org/W2065819211","https://openalex.org/W2101345238","https://openalex.org/W2153562582","https://openalex.org/W3157341860","https://openalex.org/W4242448156","https://openalex.org/W4249513058"],"related_works":["https://openalex.org/W4312590429","https://openalex.org/W3128355847","https://openalex.org/W2041077884","https://openalex.org/W4205934053","https://openalex.org/W596168634","https://openalex.org/W138666971","https://openalex.org/W2133257424","https://openalex.org/W2555215680","https://openalex.org/W2028230904","https://openalex.org/W1876423328"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":12}],"updated_date":"2026-04-20T07:46:08.049788","created_date":"2025-10-10T00:00:00"}
