{"id":"https://openalex.org/W3183630953","doi":"https://doi.org/10.3390/sym13081350","title":"Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming","display_name":"Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming","publication_year":2021,"publication_date":"2021-07-26","ids":{"openalex":"https://openalex.org/W3183630953","doi":"https://doi.org/10.3390/sym13081350","mag":"3183630953"},"language":"en","primary_location":{"id":"doi:10.3390/sym13081350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081350","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1350/pdf?version=1627373264","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/2073-8994/13/8/1350/pdf?version=1627373264","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054055136","display_name":"Mujahid Abbas","orcid":"https://orcid.org/0000-0001-5528-1207"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Mujahid Abbas","raw_affiliation_strings":["Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049752790","display_name":"Rizwan Anjum","orcid":"https://orcid.org/0000-0002-2864-6730"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rizwan Anjum","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan"],"affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021729980","display_name":"Vasile Berinde","orcid":"https://orcid.org/0000-0002-3677-795X"},"institutions":[{"id":"https://openalex.org/I158333966","display_name":"Technical University of Cluj-Napoca","ror":"https://ror.org/03r8nwp71","country_code":"RO","type":"education","lineage":["https://openalex.org/I158333966"]},{"id":"https://openalex.org/I33800924","display_name":"Academia Oamenilor de \u0218tiin\u021b\u0103 din Rom\u00e2nia","ror":"https://ror.org/04ybnj478","country_code":"RO","type":"facility","lineage":["https://openalex.org/I33800924"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Vasile Berinde","raw_affiliation_strings":["Academy of Romanian Scientists, Ilfov Str. No. 3, 50044 Bucharest, Romania","Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430122 Baia Mare, Romania"],"affiliations":[{"raw_affiliation_string":"Academy of Romanian Scientists, Ilfov Str. No. 3, 50044 Bucharest, Romania","institution_ids":["https://openalex.org/I33800924"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430122 Baia Mare, Romania","institution_ids":["https://openalex.org/I158333966"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021729980"],"corresponding_institution_ids":["https://openalex.org/I158333966","https://openalex.org/I33800924"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":9.264,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.98661417,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"13","issue":"8","first_page":"1350","last_page":"1350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9818999767303467,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.8011229634284973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7698739767074585},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.7018296122550964},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.617445707321167},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5760510563850403},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5433850884437561},{"id":"https://openalex.org/keywords/contraction-principle","display_name":"Contraction principle","score":0.49106764793395996},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4802413582801819},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.42579153180122375},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4204050898551941},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3817080855369568},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3044840097427368},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22889646887779236}],"concepts":[{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.8011229634284973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7698739767074585},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.7018296122550964},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.617445707321167},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5760510563850403},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5433850884437561},{"id":"https://openalex.org/C2775958659","wikidata":"https://www.wikidata.org/wiki/Q5165690","display_name":"Contraction principle","level":3,"score":0.49106764793395996},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4802413582801819},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.42579153180122375},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4204050898551941},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3817080855369568},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3044840097427368},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22889646887779236},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13081350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081350","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1350/pdf?version=1627373264","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:470509f1e5104a95aa7505da8fd7d82c","is_oa":true,"landing_page_url":"https://doaj.org/article/470509f1e5104a95aa7505da8fd7d82c","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 13, Iss 8, p 1350 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/8/1350/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13081350","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/sym13081350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081350","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1350/pdf?version=1627373264","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":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3183630953.pdf","grobid_xml":"https://content.openalex.org/works/W3183630953.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W154593720","https://openalex.org/W874861423","https://openalex.org/W1458771408","https://openalex.org/W1974487438","https://openalex.org/W1987050586","https://openalex.org/W2003874621","https://openalex.org/W2004325944","https://openalex.org/W2006792552","https://openalex.org/W2056368348","https://openalex.org/W2056838549","https://openalex.org/W2060568695","https://openalex.org/W2061856266","https://openalex.org/W2082113356","https://openalex.org/W2086065679","https://openalex.org/W2127473909","https://openalex.org/W2129941846","https://openalex.org/W2185271417","https://openalex.org/W2242188861","https://openalex.org/W2345736532","https://openalex.org/W2492601959","https://openalex.org/W3013846195","https://openalex.org/W3032996093","https://openalex.org/W3094484105","https://openalex.org/W3139212761","https://openalex.org/W3148142663","https://openalex.org/W3154169191","https://openalex.org/W3154956964","https://openalex.org/W3162969122","https://openalex.org/W3164354881","https://openalex.org/W3175204997","https://openalex.org/W4213383544","https://openalex.org/W4312304096","https://openalex.org/W6606292158","https://openalex.org/W6623997686","https://openalex.org/W6678252788","https://openalex.org/W6779129031","https://openalex.org/W6795788898"],"related_works":["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","https://openalex.org/W2985828462"],"abstract_inverted_index":{"The":[0],"purpose":[1],"of":[2,10,25,37,44,51,68,76,87,94,97,100],"this":[3],"paper":[4],"is":[5],"to":[6,91],"introduce":[7],"the":[8,34,69,77,88,92,95],"class":[9],"enriched":[11,19,45,82],"multivalued":[12,18,83],"contraction":[13,84],"mappings.":[14,85],"Both":[15],"single-valued":[16],"and":[17,32,39,55,73,103],"contractions":[20,46],"are":[21,106],"defined":[22],"by":[23],"means":[24],"symmetric":[26],"inequalities.":[27],"Our":[28],"main":[29],"result":[30,36],"extends":[31],"generalizes":[33],"recent":[35],"Berinde":[38],"P\u0103curar":[40],"(Approximating":[41],"fixed":[42,70,78],"points":[43],"in":[47],"Banach":[48],"spaces,":[49],"Journal":[50],"Fixed":[52],"Point":[53],"Theory":[54],"Applications,":[56],"22":[57],"(2),":[58],"1\u201310,":[59],"2020).":[60],"We":[61],"also":[62],"study":[63],"a":[64,98],"data":[65],"dependence":[66],"problem":[67,80,93],"point":[71,79],"set":[72],"Ulam\u2013Hyers":[74],"stability":[75],"for":[81],"Applications":[86],"results":[89],"obtained":[90],"existence":[96],"solution":[99],"differential":[101],"inclusions":[102],"dynamic":[104],"programming":[105],"presented.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
