{"id":"https://openalex.org/W7166568041","doi":"https://doi.org/10.48550/arxiv.2606.27517","title":"Korovkin type theorems for operators acting on functions of polynomial and exponential growth on $[0,\\infty)$","display_name":"Korovkin type theorems for operators acting on functions of polynomial and exponential growth on $[0,\\infty)$","publication_year":2026,"publication_date":"2026-06-25","ids":{"openalex":"https://openalex.org/W7166568041","doi":"https://doi.org/10.48550/arxiv.2606.27517"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2606.27517","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.27517","pdf_url":"https://arxiv.org/pdf/2606.27517","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2606.27517","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034622330","display_name":"Ulrich R. Abel","orcid":"https://orcid.org/0000-0003-1889-4850","observed_orcids":["https://orcid.org/0000-0003-1889-4850"]},"institutions":[{"id":"https://openalex.org/I45155027","display_name":"Technische Hochschule Mittelhessen","ror":"https://ror.org/02qdc9985","country_code":"DE","type":"education","lineage":["https://openalex.org/I45155027"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Abel, Ulrich","raw_affiliation_strings":["Technische Hochschule Mittelhessen , Department Mathematik , Naturwissenschaften und Datenverarbeitung , Friedberg , Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Hochschule Mittelhessen , Department Mathematik , Naturwissenschaften und Datenverarbeitung , Friedberg , Germany,","institution_ids":["https://openalex.org/I45155027"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083538592","display_name":"Ana Maria Acu","orcid":"https://orcid.org/0000-0003-1192-2281","observed_orcids":["https://orcid.org/0000-0003-1192-2281"]},"institutions":[{"id":"https://openalex.org/I124121301","display_name":"Lucian Blaga University of Sibiu","ror":"https://ror.org/026gdz537","country_code":"RO","type":"education","lineage":["https://openalex.org/I124121301"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Acu, Ana-Maria","raw_affiliation_strings":["Lucian Blaga University of Sibiu , Department of Mathematics and Informatics , Sibiu , Romania,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lucian Blaga University of Sibiu , Department of Mathematics and Informatics , Sibiu , Romania,","institution_ids":["https://openalex.org/I124121301"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036479794","display_name":"Margareta Heilmann","orcid":"https://orcid.org/0000-0002-1283-7444","observed_orcids":["https://orcid.org/0000-0002-1283-7444"]},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Heilmann, Margareta","raw_affiliation_strings":["University of Wuppertal , School of Mathematics and Natural Sciences , Wuppertal , Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wuppertal , School of Mathematics and Natural Sciences , Wuppertal , Germany,","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038657853","display_name":"Ioan Ra\u015fa","orcid":"https://orcid.org/0000-0002-5206-030X","observed_orcids":["https://orcid.org/0000-0002-5206-030X"]},"institutions":[{"id":"https://openalex.org/I158333966","display_name":"Technical University of Cluj-Napoca","ror":"https://ror.org/03r8nwp71","country_code":"RO","type":"education","lineage":["https://openalex.org/I158333966"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Rasa, Ioan","raw_affiliation_strings":["Technical University of Cluj-Napoca , Department of Mathematics , Cluj-Napoca , Romania,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Cluj-Napoca , Department of Mathematics , Cluj-Napoca , Romania,","institution_ids":["https://openalex.org/I158333966"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":1.0,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":1.0,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0,"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":0.0,"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/korovkin-type-theorems","display_name":"Korovkin-type theorems","score":0.8970000147819519},{"id":"https://openalex.org/keywords/positive-linear-operators","display_name":"positive linear operators","score":0.9950000047683716},{"id":"https://openalex.org/keywords/pointwise-convergence","display_name":"pointwise convergence","score":0.6899999976158142},{"id":"https://openalex.org/keywords/polynomial-growth","display_name":"polynomial growth","score":0.7540000081062317},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"exponential growth","score":0.9990000128746033},{"id":"https://openalex.org/keywords/baskakov-operators","display_name":"Baskakov operators","score":0.8629999756813049},{"id":"https://openalex.org/keywords/szasz-mirakjan-operators","display_name":"Sz\u00e1sz-Mirakjan operators","score":0.9359999895095825},{"id":"https://openalex.org/keywords/benchmark-functions","display_name":"benchmark functions","score":0.7450000047683716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8611000180244446},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.7612000107765198},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7016000151634216},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6538000106811523},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6518999934196472},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.5902000069618225},{"id":"https://openalex.org/C101346110","wikidata":"https://www.wikidata.org/wiki/Q4867603","display_name":"Baskakov operator","level":5,"score":0.5364000201225281},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5095000267028809},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49320000410079956},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48330000042915344},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45559999346733093},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.4481000006198883},{"id":"https://openalex.org/C103642545","wikidata":"https://www.wikidata.org/wiki/Q5421531","display_name":"Exponential type","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.40779998898506165},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37310001254081726},{"id":"https://openalex.org/C85384003","wikidata":"https://www.wikidata.org/wiki/Q5421525","display_name":"Exponential polynomial","level":3,"score":0.3659000098705292},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3240000009536743},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26190000772476196},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.2549000084400177}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2606.27517","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.27517","pdf_url":"https://arxiv.org/pdf/2606.27517","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2606.27517","doi":"https://doi.org/10.48550/arxiv.2606.27517","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27517","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2606.27517","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.27517","pdf_url":"https://arxiv.org/pdf/2606.27517","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7166568041.pdf","grobid_xml":"https://content.openalex.org/works/W7166568041.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2896328136","https://openalex.org/W2092453948","https://openalex.org/W7098013471","https://openalex.org/W3004417559","https://openalex.org/W4283586897","https://openalex.org/W2163501389","https://openalex.org/W2566652679","https://openalex.org/W4401265331","https://openalex.org/W2809365083","https://openalex.org/W7125141034"],"abstract_inverted_index":{"We":[0],"establish":[1],"two":[2],"Korovkin-type":[3],"approximation":[4],"theorems":[5],"for":[6,33,52,107],"sequences":[7],"of":[8,54],"positive":[9,75],"linear":[10,76],"operators":[11,92],"acting":[12],"on":[13,16,25,111,116],"continuous":[14],"functions":[15,29,53,60,97],"$[0,\\infty)$.":[17],"The":[18,45,66,101],"first":[19],"result":[20,47],"shows":[21],"that":[22,39],"pointwise":[23,31,109],"convergence":[24,32,110,115],"all":[26],"polynomial":[27],"test":[28,59,118],"implies":[30],"every":[34],"function":[35],"in":[36],"the":[37,58,62],"domain":[38],"is":[40],"dominated":[41],"by":[42],"a":[43,104],"polynomial.":[44],"second":[46],"provides":[48,103],"an":[49],"analogous":[50],"criterion":[51],"exponential":[55],"growth,":[56],"where":[57],"are":[61,68,89],"exponentials":[63],"$e^{\u03bbx}$,":[64],"$\u03bb\\in\\mathbb{R}$.":[65],"results":[67],"applied":[69],"to":[70,91],"several":[71],"classical":[72],"and":[73,84,98],"modified":[74,95],"operators,":[77],"including":[78],"Baskakov,":[79],"Sz\u00e1sz--Mirakjan,":[80],"Phillips,":[81],"Post--Widder,":[82],"Gamma,":[83],"Durrmeyer-type":[85],"operators.":[86],"Further":[87],"applications":[88],"given":[90],"associated":[93],"with":[94],"Bessel":[96],"hyperbolic":[99],"functions.":[100,119],"approach":[102],"unified":[105],"framework":[106],"deriving":[108],"unbounded":[112],"intervals":[113],"from":[114],"suitable":[117]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-06-30T00:00:00"}