{"id":"https://openalex.org/W4402969420","doi":"https://doi.org/10.1007/s00211-024-01434-7","title":"A generalization of a theorem of Brass and Schmeisser","display_name":"A generalization of a theorem of Brass and Schmeisser","publication_year":2024,"publication_date":"2024-09-30","ids":{"openalex":"https://openalex.org/W4402969420","doi":"https://doi.org/10.1007/s00211-024-01434-7"},"language":"lv","primary_location":{"id":"doi:10.1007/s00211-024-01434-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-024-01434-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01434-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01434-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052177694","display_name":"Tomasz Szostok","orcid":"https://orcid.org/0000-0001-5965-5042"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I864159182","display_name":"University of Silesia in Katowice","ror":"https://ror.org/0104rcc94","country_code":"PL","type":"education","lineage":["https://openalex.org/I864159182"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Tomasz Szostok","raw_affiliation_strings":["Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland","institution_ids":["https://openalex.org/I864159182","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052177694"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I864159182"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":4.0414,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.94113792,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"156","issue":"5","first_page":"1915","last_page":"1925"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998000264167786,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998000264167786,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9998000264167786,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8106842041015625},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7109742760658264},{"id":"https://openalex.org/keywords/brass","display_name":"Brass","score":0.6241915225982666},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42358261346817017},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.38832056522369385},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3674575686454773},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34099531173706055},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3257354497909546},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29958927631378174}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8106842041015625},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7109742760658264},{"id":"https://openalex.org/C2780033417","wikidata":"https://www.wikidata.org/wiki/Q39782","display_name":"Brass","level":3,"score":0.6241915225982666},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42358261346817017},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.38832056522369385},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3674575686454773},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34099531173706055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3257354497909546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29958927631378174},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C544778455","wikidata":"https://www.wikidata.org/wiki/Q753","display_name":"Copper","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-024-01434-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-024-01434-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01434-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00211-024-01434-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-024-01434-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01434-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4402969420.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1988727093","https://openalex.org/W2002749406","https://openalex.org/W2009207747","https://openalex.org/W2110488052","https://openalex.org/W2336151066","https://openalex.org/W2463753824","https://openalex.org/W2527497445","https://openalex.org/W2585926046","https://openalex.org/W2791583120","https://openalex.org/W2963832135","https://openalex.org/W3092637309","https://openalex.org/W3115781974","https://openalex.org/W3195149909","https://openalex.org/W4292070096"],"related_works":["https://openalex.org/W4250111590","https://openalex.org/W2049376157","https://openalex.org/W2184197376","https://openalex.org/W4252135359","https://openalex.org/W4247323958","https://openalex.org/W1997757973","https://openalex.org/W2054806274","https://openalex.org/W2389958343","https://openalex.org/W4245106673","https://openalex.org/W2904662751"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"n":[2,146,153],"be":[3],"an":[4,134],"odd":[5],"positive":[6,61,149],"integer.":[7],"It":[8],"was":[9],"proved":[10],"by":[11,133],"Brass":[12],"and":[13,76,103,142,158],"Schmeisser":[14],"that":[15],"for":[16,77,118],"every":[17,78],"quadrature":[18],"$$\\mathcal":[19],"{Q}=\\alpha":[20],"_1f(x_1)+\\dots":[21],"+\\alpha":[22],"_mf(x_m)$$":[23],"<mml:math":[24,68,80,109],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[25,69,81,110],"<mml:mrow>":[26,34,50,70,82,111],"<mml:mi>Q</mml:mi>":[27],"<mml:mo>=</mml:mo>":[28],"<mml:msub>":[29,36,45,52],"<mml:mi>\u03b1</mml:mi>":[30,46],"<mml:mn>1</mml:mn>":[31,38,73,114],"</mml:msub>":[32,39,48,55],"<mml:mi>f</mml:mi>":[33,49],"<mml:mo>(</mml:mo>":[35,51],"<mml:mi>x</mml:mi>":[37,53],"<mml:mo>)</mml:mo>":[40,56],"</mml:mrow>":[41,57,58,74,85,115],"<mml:mo>+</mml:mo>":[42,44,72,113],"<mml:mo>\u22ef</mml:mo>":[43],"<mml:mi>m</mml:mi>":[47,54],"</mml:math>":[59,75,86,116],"(with":[60],"weights)":[62],"of":[63,93,101,106],"order":[64,107],"at":[65],"least":[66],"$$n+1$$":[67,108],"<mml:mi>n</mml:mi>":[71,83,112],"$$n-$$":[79],"<mml:mo>-</mml:mo>":[84],"convex":[87],"function":[88,121],"f":[89,96,122],",":[90],"the":[91,99,119,144],"value":[92],"Q":[94,132],"on":[95],"lies":[97],"between":[98],"values":[100],"Gauss-Legendre":[102,157],"Gauss-Lobatto":[104,159],"quadratures":[105,155],"calculated":[117],"same":[120],".":[123],"We":[124],"generalize":[125],"this":[126],"result":[127],"in":[128],"two":[129],"directions,":[130],"replacing":[131],"integral":[135],"with":[136],"respect":[137],"to":[138,147],"a":[139],"given":[140],"measure":[141],"allowing":[143],"number":[145],"any":[148],"integer":[150],"(for":[151],"even":[152],"Gauss-Radau":[154],"replace":[156],"ones).":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}