{"id":"https://openalex.org/W2885400759","doi":"https://doi.org/10.1090/mcom/3396","title":"Difference inequalities and barycentric identities for classical discrete iterated weights","display_name":"Difference inequalities and barycentric identities for classical discrete iterated weights","publication_year":2018,"publication_date":"2018-08-15","ids":{"openalex":"https://openalex.org/W2885400759","doi":"https://doi.org/10.1090/mcom/3396","mag":"2885400759"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3396","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3396","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03396-8/S0025-5718-2018-03396-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03396-8/S0025-5718-2018-03396-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028757461","display_name":"Przemys\u0142aw Rutka","orcid":"https://orcid.org/0000-0003-4712-2710"},"institutions":[{"id":"https://openalex.org/I111702420","display_name":"John Paul II Catholic University of Lublin","ror":"https://ror.org/04qyefj88","country_code":"PL","type":"education","lineage":["https://openalex.org/I111702420"]},{"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"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Przemys\u0142aw Rutka","raw_affiliation_strings":["Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00c3\u00b3w 1H, 20-708 Lublin, Poland","Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00f3w 1H, 20-708 Lublin, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00c3\u00b3w 1H, 20-708 Lublin, Poland","institution_ids":["https://openalex.org/I111702420","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00f3w 1H, 20-708 Lublin, Poland","institution_ids":["https://openalex.org/I111702420","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067044096","display_name":"Ryszard Smarzewski","orcid":"https://orcid.org/0000-0001-5754-5747"},"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/I111702420","display_name":"John Paul II Catholic University of Lublin","ror":"https://ror.org/04qyefj88","country_code":"PL","type":"education","lineage":["https://openalex.org/I111702420"]},{"id":"https://openalex.org/I4210156473","display_name":"Pa\u0144stwowa Wy\u017csza Szko\u0142a Zawodowa we W\u0142oc\u0142awku","ror":"https://ror.org/053ya0s96","country_code":"PL","type":"education","lineage":["https://openalex.org/I4210156473"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Ryszard Smarzewski","raw_affiliation_strings":["Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00c3\u00b3w 1H, 20-708 Lublin, Poland","PWSZ W\u00c5\u0082oc\u00c5\u0082awek, ul. 3 Maja 17, 87-800 W\u00c5\u0082oc\u00c5\u0082awek, Poland","Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00f3w 1H, 20-708 Lublin, Poland","PWSZ W\u0142oc\u0142awek, ul. 3 Maja 17, 87-800 W\u0142oc\u0142awek, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00c3\u00b3w 1H, 20-708 Lublin, Poland","institution_ids":["https://openalex.org/I111702420","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"PWSZ W\u00c5\u0082oc\u00c5\u0082awek, ul. 3 Maja 17, 87-800 W\u00c5\u0082oc\u00c5\u0082awek, Poland","institution_ids":["https://openalex.org/I4210156473"]},{"raw_affiliation_string":"Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, ul. Konstantyn\u00f3w 1H, 20-708 Lublin, Poland","institution_ids":["https://openalex.org/I111702420","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"PWSZ W\u0142oc\u0142awek, ul. 3 Maja 17, 87-800 W\u0142oc\u0142awek, Poland","institution_ids":["https://openalex.org/I4210156473"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028757461"],"corresponding_institution_ids":["https://openalex.org/I111702420","https://openalex.org/I4210137370"],"apc_list":null,"apc_paid":null,"fwci":1.3724,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79098594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"88","issue":"318","first_page":"1791","last_page":"1804"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9990000128746033,"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":0.9990000128746033,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9929999709129333,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9914000034332275,"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/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.9575198888778687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9384373426437378},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6748551726341248},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5924918055534363},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4524768590927124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3653492331504822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17900827527046204}],"concepts":[{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.9575198888778687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9384373426437378},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6748551726341248},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5924918055534363},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4524768590927124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3653492331504822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17900827527046204}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3396","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3396","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03396-8/S0025-5718-2018-03396-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/mcom/3396","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3396","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03396-8/S0025-5718-2018-03396-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2885400759.pdf","grobid_xml":"https://content.openalex.org/works/W2885400759.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W190006759","https://openalex.org/W878304541","https://openalex.org/W1528387448","https://openalex.org/W1966268321","https://openalex.org/W1985674015","https://openalex.org/W1986280275","https://openalex.org/W2003452159","https://openalex.org/W2008262009","https://openalex.org/W2019646583","https://openalex.org/W2023376265","https://openalex.org/W2034008227","https://openalex.org/W2044788680","https://openalex.org/W2065334415","https://openalex.org/W2066611119","https://openalex.org/W2085301483","https://openalex.org/W2092611097","https://openalex.org/W2163776761","https://openalex.org/W2165237086","https://openalex.org/W2316418224","https://openalex.org/W2568753013","https://openalex.org/W2588166938","https://openalex.org/W2788840278","https://openalex.org/W3038165843"],"related_works":["https://openalex.org/W1837290348","https://openalex.org/W3046826018","https://openalex.org/W2078096344","https://openalex.org/W2258456823","https://openalex.org/W2549622050","https://openalex.org/W4235859817","https://openalex.org/W2137742453","https://openalex.org/W2153764672","https://openalex.org/W1812460224","https://openalex.org/W2029790925"],"abstract_inverted_index":{"In":[0,105],"this":[1],"paper":[2],"we":[3],"characterize":[4],"extremal":[5],"polynomials":[6],"and":[7,102,120,146,155,160,163],"the":[8,12,61,70,75,83,94,112,116,135,138,147],"best":[9,84],"constants":[10,85],"for":[11,86,126],"Szeg\u00c5\u0091\u00e2\u0080\u0093Markov\u00e2\u0080\u0093Bernstein-type":[13],"inequalities,":[14],"associated":[15],"with":[16],"iterated":[17],"weight":[18,38,130],"functions":[19],"$\\rho":[20,39],"_{k}\\left":[21],"(":[22,27,32,41,47],"x\\right":[23,42,48],")":[24,29,43],"\\!=\\!":[25],"A\\left":[26],"x+h\\right":[28,33],"\\rho":[30,45],"_{k-1}\\left":[31],")$":[34,49],"of":[35,50,63,69,82,93,123],"any":[36],"classical":[37,91,128],"_{0}\\left":[40],"=":[44,54],"\\left":[46],"discrete":[51,90,129,136],"variable":[52],"$x":[53],"a+ih$,":[55],"which":[56,132],"is":[57],"defined":[58],"to":[59,78,110,134,142],"be":[60],"solution":[62],"a":[64],"difference":[65],"boundary":[66],"value":[67],"problem":[68],"Pearson":[71],"type.":[72],"It":[73],"yields":[74],"effective":[76],"way":[77],"compute":[79],"numerical":[80],"values":[81],"all":[87],"six":[88],"basic":[89],"weights":[92],"Charlier,":[95],"Meixner,":[96],"Kravchuk,":[97],"Hahn":[98,100],"I,":[99],"II,":[101],"Chebyshev":[103],"kind.":[104],"addition,":[106],"it":[107],"enables":[108],"us":[109],"establish":[111],"generic":[113],"identities":[114],"between":[115],"Lagrange":[117],"barycentric":[118],"coefficients":[119],"Christoffel":[121],"numbers":[122],"Gauss":[124],"quadratures":[125],"these":[127],"functions,":[131],"extends":[133],"case":[137],"recent":[139],"results":[140],"due":[141],"Wang":[143],"et":[144],"al.":[145],"authors,":[148],"published":[149],"in":[150],"[Math.":[151,164],"Comp.":[152,165],"81":[153],"(2012)":[154],"83":[156],"(2014),":[157],"pp.":[158,168],"861\u00e2\u0080\u0093877":[159],"2893\u00e2\u0080\u00932914,":[161],"respectively]":[162],"86":[166],"(2017),":[167],"2409\u00e2\u0080\u00932427].":[169]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}