{"id":"https://openalex.org/W4393255343","doi":"https://doi.org/10.3390/axioms13040225","title":"Weak Sharp Type Solutions for Some Variational Integral Inequalities","display_name":"Weak Sharp Type Solutions for Some Variational Integral Inequalities","publication_year":2024,"publication_date":"2024-03-28","ids":{"openalex":"https://openalex.org/W4393255343","doi":"https://doi.org/10.3390/axioms13040225"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13040225","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13040225","pdf_url":"https://www.mdpi.com/2075-1680/13/4/225/pdf?version=1711628585","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/2075-1680/13/4/225/pdf?version=1711628585","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046581790","display_name":"Savin Trean\u0163\u0103","orcid":"https://orcid.org/0000-0001-8209-3869"},"institutions":[{"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"]},{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Savin Trean\u0163\u0103","raw_affiliation_strings":["Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania","Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania","Fundamental Sciences Applied in Engineering-Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0001-8209-3869","affiliations":[{"raw_affiliation_string":"Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania","institution_ids":["https://openalex.org/I33800924"]},{"raw_affiliation_string":"Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]},{"raw_affiliation_string":"Fundamental Sciences Applied in Engineering-Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012641009","display_name":"Tareq Saeed","orcid":"https://orcid.org/0000-0002-0170-5286"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tareq Saeed","raw_affiliation_strings":["Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia","Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics,"],"raw_orcid":"https://orcid.org/0000-0002-0170-5286","affiliations":[{"raw_affiliation_string":"Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics,","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046581790"],"corresponding_institution_ids":["https://openalex.org/I33800924","https://openalex.org/I61641377"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.3316,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56789737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":"4","first_page":"225","last_page":"225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9998999834060669,"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":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9987000226974487,"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/type","display_name":"Type (biology)","score":0.6896141171455383},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6608515381813049},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6228001713752747},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.5426846146583557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4276151955127716},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40601417422294617},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33980411291122437},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3325516879558563},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.09241247177124023},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07356107234954834}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6896141171455383},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6608515381813049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6228001713752747},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5426846146583557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4276151955127716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40601417422294617},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33980411291122437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3325516879558563},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09241247177124023},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07356107234954834},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13040225","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13040225","pdf_url":"https://www.mdpi.com/2075-1680/13/4/225/pdf?version=1711628585","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:7fd510fcff4341b18a7cf8e6b6ff7881","is_oa":true,"landing_page_url":"https://doaj.org/article/7fd510fcff4341b18a7cf8e6b6ff7881","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 13, Iss 4, p 225 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13040225","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13040225","pdf_url":"https://www.mdpi.com/2075-1680/13/4/225/pdf?version=1711628585","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":[{"score":0.6399999856948853,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4393255343.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W416122618","https://openalex.org/W657454232","https://openalex.org/W1503425191","https://openalex.org/W1976772621","https://openalex.org/W2006011805","https://openalex.org/W2064114733","https://openalex.org/W2067462059","https://openalex.org/W2068219379","https://openalex.org/W2091972146","https://openalex.org/W2109529500","https://openalex.org/W2237636956","https://openalex.org/W2744494937","https://openalex.org/W2765970199","https://openalex.org/W2792996412","https://openalex.org/W3027783027","https://openalex.org/W3029515389","https://openalex.org/W3128419426","https://openalex.org/W3157991665","https://openalex.org/W3162518040","https://openalex.org/W3186638068","https://openalex.org/W4210909659","https://openalex.org/W4241705128","https://openalex.org/W4312075633","https://openalex.org/W4379798148","https://openalex.org/W4387826921","https://openalex.org/W6857793314"],"related_works":["https://openalex.org/W2909053289","https://openalex.org/W829267240","https://openalex.org/W1154119719","https://openalex.org/W3131922696","https://openalex.org/W2104243281","https://openalex.org/W2946037075","https://openalex.org/W2755725405","https://openalex.org/W1967850176","https://openalex.org/W2011180822","https://openalex.org/W2061987434"],"abstract_inverted_index":{"Weak":[0],"sharp":[1],"type":[2],"solutions":[3],"are":[4],"analyzed":[5],"for":[6],"a":[7,13],"variational":[8],"integral":[9,19],"inequality":[10],"defined":[11],"by":[12],"convex":[14],"functional":[15],"of":[16],"the":[17,24,29],"multiple":[18],"type.":[20],"A":[21],"connection":[22],"with":[23,28],"sufficiency":[25],"property":[26],"associated":[27],"minimum":[30],"principle":[31],"is":[32,41],"formulated,":[33],"as":[34],"well.":[35],"Also,":[36],"an":[37],"illustrative":[38],"numerical":[39],"application":[40],"provided.":[42]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
