{"id":"https://openalex.org/W2116853550","doi":"https://doi.org/10.1155/s0161171204208080","title":"On Volterra inequalities and their applications","display_name":"On Volterra inequalities and their applications","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2116853550","doi":"https://doi.org/10.1155/s0161171204208080","mag":"2116853550"},"language":"en","primary_location":{"id":"doi:10.1155/s0161171204208080","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204208080","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/217479.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2004/217479.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000638717","display_name":"Lechos\u0142aw H\u0105cia","orcid":null},"institutions":[{"id":"https://openalex.org/I46597724","display_name":"Pozna\u0144 University of Technology","ror":"https://ror.org/00p7p3302","country_code":"PL","type":"education","lineage":["https://openalex.org/I46597724"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Lechos\u0142aw H\u0105cia","raw_affiliation_strings":["Institute of Mathematics, Pozna\u0144 University of Technology, Piotrowo 3a"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Pozna\u0144 University of Technology, Piotrowo 3a","institution_ids":["https://openalex.org/I46597724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000638717"],"corresponding_institution_ids":["https://openalex.org/I46597724"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.19710744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2004","issue":"3","first_page":"117","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.991599977016449,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.991599977016449,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9758999943733215,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9684000015258789,"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":0.8525106906890869},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.7406361103057861},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5108456015586853},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.49003279209136963},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4862762689590454},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3742576837539673},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3674467206001282},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3386036157608032},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32203418016433716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8525106906890869},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.7406361103057861},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5108456015586853},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.49003279209136963},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4862762689590454},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3742576837539673},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3674467206001282},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3386036157608032},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32203418016433716},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/s0161171204208080","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204208080","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/217479.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:217479","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2004/217479.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:03c0e27e06694d6082ec451ce63f86e9","is_oa":true,"landing_page_url":"https://doaj.org/article/03c0e27e06694d6082ec451ce63f86e9","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 3, Pp 117-134 (2004)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/S0161171204208080","is_oa":false,"landing_page_url":"https://doi.org/10.1155/S0161171204208080","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1155/s0161171204208080","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204208080","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/217479.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5699999928474426,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2116853550.pdf","grobid_xml":"https://content.openalex.org/works/W2116853550.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W590529998","https://openalex.org/W1574435983","https://openalex.org/W2062028320","https://openalex.org/W2134184306","https://openalex.org/W2783512713","https://openalex.org/W4302562054"],"related_works":["https://openalex.org/W2517687681","https://openalex.org/W2118560105","https://openalex.org/W2358959122","https://openalex.org/W4225984655","https://openalex.org/W2031624200","https://openalex.org/W1539637428","https://openalex.org/W1541040149","https://openalex.org/W1826865795","https://openalex.org/W2754932876","https://openalex.org/W325682659"],"abstract_inverted_index":{"We":[0],"present":[1],"certain":[2],"variants":[3],"of":[4,15],"two\u2010dimensional":[5],"and":[6,30],"n":[7],"\u2010dimensional":[8],"Volterra":[9],"integral":[10,31],"inequalities.":[11],"In":[12],"particular,":[13],"generalizations":[14],"the":[16],"Gronwall":[17],"inequality":[18],"are":[19,23],"obtained.":[20],"These":[21],"results":[22],"applied":[24],"in":[25],"various":[26],"problems":[27],"for":[28],"differential":[29],"equations.":[32]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}