{"id":"https://openalex.org/W2012726354","doi":"https://doi.org/10.1155/2013/159720","title":"A Survey of Results on the Limit -Bernstein Operator","display_name":"A Survey of Results on the Limit -Bernstein Operator","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2012726354","doi":"https://doi.org/10.1155/2013/159720","mag":"2012726354"},"language":"en","primary_location":{"id":"doi:10.1155/2013/159720","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/159720","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/159720.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","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/jam/2013/159720.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102758527","display_name":"Sofiya Ostrovska","orcid":null},"institutions":[{"id":"https://openalex.org/I45542416","display_name":"Atilim University","ror":"https://ror.org/04pd3v454","country_code":"TR","type":"education","lineage":["https://openalex.org/I45542416"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Sofiya Ostrovska","raw_affiliation_strings":["Department of Mathematics, Atilim University, Ankara 06836, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-0447-4591","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Atilim University, Ankara 06836, Turkey","institution_ids":["https://openalex.org/I45542416"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102758527"],"corresponding_institution_ids":["https://openalex.org/I45542416"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.2968,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62254179,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9718000292778015,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9656000137329102,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/operator","display_name":"Operator (biology)","score":0.7067739963531494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6742266416549683},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6243279576301575},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5646592974662781},{"id":"https://openalex.org/keywords/pseudo-monotone-operator","display_name":"Pseudo-monotone operator","score":0.5578812956809998},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5222000479698181},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5167316794395447},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.5098070502281189},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.48097172379493713},{"id":"https://openalex.org/keywords/ladder-operator","display_name":"Ladder operator","score":0.4562358856201172},{"id":"https://openalex.org/keywords/multiplication-operator","display_name":"Multiplication operator","score":0.438533216714859},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.43713611364364624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35553887486457825},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.30579817295074463},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1823558211326599},{"id":"https://openalex.org/keywords/operator-space","display_name":"Operator space","score":0.14357483386993408},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.1196536123752594},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.10778987407684326},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08728751540184021}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7067739963531494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6742266416549683},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6243279576301575},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5646592974662781},{"id":"https://openalex.org/C201040074","wikidata":"https://www.wikidata.org/wiki/Q7254436","display_name":"Pseudo-monotone operator","level":5,"score":0.5578812956809998},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5222000479698181},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5167316794395447},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.5098070502281189},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.48097172379493713},{"id":"https://openalex.org/C134440745","wikidata":"https://www.wikidata.org/wiki/Q1186765","display_name":"Ladder operator","level":4,"score":0.4562358856201172},{"id":"https://openalex.org/C82916341","wikidata":"https://www.wikidata.org/wiki/Q6934990","display_name":"Multiplication operator","level":3,"score":0.438533216714859},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.43713611364364624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35553887486457825},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.30579817295074463},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1823558211326599},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.14357483386993408},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.1196536123752594},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.10778987407684326},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08728751540184021},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/159720","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/159720","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/159720.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394807912","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394807912","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:e288714b1106445d8019ab0d90160063","is_oa":true,"landing_page_url":"https://doaj.org/article/e288714b1106445d8019ab0d90160063","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":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/159720","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/159720","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/159720.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8899999856948853,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323146","display_name":"Atilim \u00dcniversitesi","ror":"https://ror.org/04pd3v454"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2012726354.pdf","grobid_xml":"https://content.openalex.org/works/W2012726354.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W187372960","https://openalex.org/W1672897283","https://openalex.org/W1760824630","https://openalex.org/W1971507256","https://openalex.org/W1971853184","https://openalex.org/W1976420751","https://openalex.org/W1982973268","https://openalex.org/W1987981292","https://openalex.org/W1991983106","https://openalex.org/W1995952566","https://openalex.org/W2007251167","https://openalex.org/W2012929004","https://openalex.org/W2014677899","https://openalex.org/W2017628160","https://openalex.org/W2034186894","https://openalex.org/W2037238787","https://openalex.org/W2045068834","https://openalex.org/W2048874022","https://openalex.org/W2064399544","https://openalex.org/W2075531359","https://openalex.org/W2075960094","https://openalex.org/W2076024609","https://openalex.org/W2084049515","https://openalex.org/W2085452374","https://openalex.org/W2086260440","https://openalex.org/W2119714939","https://openalex.org/W2139344815","https://openalex.org/W2157639941","https://openalex.org/W2253988226","https://openalex.org/W2263192437","https://openalex.org/W2564314320","https://openalex.org/W2751862591","https://openalex.org/W3028381806","https://openalex.org/W3104497548","https://openalex.org/W4240644230","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2202672589","https://openalex.org/W4384156172","https://openalex.org/W2902029592","https://openalex.org/W2387730447","https://openalex.org/W2387027204","https://openalex.org/W2377566525","https://openalex.org/W1507283528","https://openalex.org/W2375960143","https://openalex.org/W4285413429","https://openalex.org/W4300046034"],"abstract_inverted_index":{"The":[0],"limit":[1,69,127],"-Bernstein":[2,70,128],"operator":[3,12,42,71,89,129],"emerges":[4],"naturally":[5],"as":[6,51],"a":[7,31,44,85,109,120],"modification":[8],"of":[9,33,58,61,100,108,122],"the":[10,15,22,27,34,38,48,56,59,62,65,68,98,103,106,123,126,132],"Sz\u00e1sz-Mirakyan":[11],"related":[13,130],"to":[14,25,131],"Euler":[16],"distribution,":[17],"which":[18],"is":[19,84,138],"used":[20],"in":[21,30,47],"-boson":[23],"theory":[24,50],"describe":[26],"energy":[28],"distribution":[29],"-analogue":[32],"coherent":[35],"state.":[36],"At":[37],"same":[39],"time,":[40],"this":[41,116],"bears":[43],"significant":[45],"role":[46],"approximation":[49,94,133],"an":[52],"exemplary":[53],"model":[54],"for":[55],"study":[57],"convergence":[60],"-operators.":[63],"Over":[64],"past":[66],"years,":[67],"has":[72,80],"been":[73,81,113],"studied":[74],"widely":[75],"from":[76],"different":[77],"perspectives.":[78],"It":[79],"shown":[82],"that":[83],"positive":[86],"shape-preserving":[87],"linear":[88],"on":[90,105,125],"with":[91],".":[92],"Its":[93],"properties,":[95],"probabilistic":[96],"interpretation,":[97],"behavior":[99],"iterates,":[101],"and":[102],"impact":[104],"smoothness":[107],"function":[110],"have":[111],"already":[112],"examined.":[114],"In":[115],"paper,":[117],"we":[118],"present":[119],"review":[121],"results":[124],"theory.":[134],"A":[135],"complete":[136],"bibliography":[137],"supplied.":[139]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
