{"id":"https://openalex.org/W1965537246","doi":"https://doi.org/10.1080/00207160701882121","title":"On the bounded derivatives of the solutions of the linear Volterra integral equations","display_name":"On the bounded derivatives of the solutions of the linear Volterra integral equations","publication_year":2008,"publication_date":"2008-07-15","ids":{"openalex":"https://openalex.org/W1965537246","doi":"https://doi.org/10.1080/00207160701882121","mag":"1965537246"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701882121","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701882121","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5062753782","display_name":"\u00d6. Faruk Temizer","orcid":null},"institutions":[{"id":"https://openalex.org/I20126385","display_name":"Inonu University","ror":"https://ror.org/04asck240","country_code":"TR","type":"education","lineage":["https://openalex.org/I20126385"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"\u00d6. Faruk Temizer","raw_affiliation_strings":["\u0130n\u00f6nu\u00a8 U\u00a8niversitesi , E\u011fitim Fak\u00fcltesi, Malatya, Turkey"],"affiliations":[{"raw_affiliation_string":"\u0130n\u00f6nu\u00a8 U\u00a8niversitesi , E\u011fitim Fak\u00fcltesi, Malatya, Turkey","institution_ids":["https://openalex.org/I20126385"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100992772","display_name":"\u0130smet \u00d6zdemir","orcid":null},"institutions":[{"id":"https://openalex.org/I20126385","display_name":"Inonu University","ror":"https://ror.org/04asck240","country_code":"TR","type":"education","lineage":["https://openalex.org/I20126385"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"\u0130smet \u00d6zdemir","raw_affiliation_strings":["\u0130n\u00f6nu\u00a8 U\u00a8niversitesi , E\u011fitim Fak\u00fcltesi, Malatya, Turkey"],"affiliations":[{"raw_affiliation_string":"\u0130n\u00f6nu\u00a8 U\u00a8niversitesi , E\u011fitim Fak\u00fcltesi, Malatya, Turkey","institution_ids":["https://openalex.org/I20126385"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062753782"],"corresponding_institution_ids":["https://openalex.org/I20126385"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.05225945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"86","issue":"9","first_page":"1512","last_page":"1541"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9902999997138977,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9822999835014343,"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":0.8852747678756714},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.82212233543396},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.7061846852302551},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5847448110580444},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5744994282722473},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5443780422210693},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.48374080657958984},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.46078383922576904},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.45466747879981995},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.4414898157119751},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2970249056816101}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8852747678756714},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.82212233543396},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.7061846852302551},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5847448110580444},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5744994282722473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5443780422210693},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48374080657958984},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.46078383922576904},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.45466747879981995},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4414898157119751},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2970249056816101},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701882121","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701882121","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1981395473","https://openalex.org/W1997085769","https://openalex.org/W2004648346","https://openalex.org/W2014172170","https://openalex.org/W2020469686","https://openalex.org/W2067974659","https://openalex.org/W2079124418","https://openalex.org/W2482061462","https://openalex.org/W4293087381"],"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/W1826865795","https://openalex.org/W2754932876","https://openalex.org/W325682659","https://openalex.org/W3130959766","https://openalex.org/W2014667605"],"abstract_inverted_index":{"The":[0,68,104],"boundaries":[1,105,133],"for":[2,74,145],"the":[3,6,12,16,76,83,107,110,132,135,148,151],"solution":[4,84,149],"of":[5,11,15,40,54,82,85,106,109,134,147,150],"linear":[7,111],"Volterra":[8,41,112],"integral":[9,56,113],"equations":[10,39,114],"second":[13],"type":[14],"form":[17],"with":[18,115],"unit":[19],"source":[20],"term":[21],"and":[22,33,92,100],"positive":[23],"monotonically":[24],"increasing":[25],"convolution":[26,116],"kernel":[27],"were":[28,88],"obtained":[29],"as":[30,79],"|f(t)|\u22641,":[31],"|f(t)|\u22642":[32,80],"|f(t)|\u22644":[34],"in":[35],"[R.":[36],"Ling,":[37,52],"Integral":[38],"type,":[42],"J.":[43,59],"Math.":[44,60,62,118],"Anal.":[45],"Appl.":[46],"64":[47],"(1978),":[48],"pp.":[49,66,122],"381\u2013397,":[50],"R.":[51],"Solutions":[53],"singular":[55],"equations,":[57],"Internat.":[58],"&":[61],"Sci.":[63],"5":[64],"(1982),":[65],"123\u2013131.].":[67],"sufficient":[69],"conditions":[70],"which":[71,129],"are":[72],"useful":[73],"finding":[75,131],"boundary":[77],"such":[78],"n":[81,93],"this":[86,125],"equation":[87,153],"given,":[89],"where":[90],"0\u2264t<\u221e":[91],"is":[94],"a":[95,127],"natural":[96],"number,":[97],"[\u0130.":[98],"\u00d6zdemir":[99],"\u00d6.":[101],"F.":[102],"Temizer,":[103],"solutions":[108],"kernel,":[117],"Comp.":[119],"75":[120],"(2006),":[121],"1175\u20131199.].":[123],"In":[124],"paper,":[126],"method":[128],"ensures":[130],"derivative":[136],"functions":[137],"f":[138,140,143],"\u2032,":[139],"\u2032\u2032,":[141],"\u2026,":[142],"(n+2)":[144],"n\u2208\u2115":[146],"same":[152],"has":[154],"been":[155],"developed.":[156]},"counts_by_year":[{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
