{"id":"https://openalex.org/W4312186348","doi":"https://doi.org/10.3390/axioms12010005","title":"Approximation Properties of the Blending-Type Bernstein\u2013Durrmeyer Operators","display_name":"Approximation Properties of the Blending-Type Bernstein\u2013Durrmeyer Operators","publication_year":2022,"publication_date":"2022-12-21","ids":{"openalex":"https://openalex.org/W4312186348","doi":"https://doi.org/10.3390/axioms12010005"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12010005","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010005","pdf_url":"https://www.mdpi.com/2075-1680/12/1/5/pdf?version=1673509809","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/1/5/pdf?version=1673509809","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100454948","display_name":"Yujie Liu","orcid":"https://orcid.org/0000-0002-4080-229X"},"institutions":[{"id":"https://openalex.org/I46482218","display_name":"Anqing Normal University","ror":"https://ror.org/0127ytz78","country_code":"CN","type":"education","lineage":["https://openalex.org/I46482218"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Jie Liu","raw_affiliation_strings":["School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China","institution_ids":["https://openalex.org/I46482218"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082203192","display_name":"Wen-Tao Cheng","orcid":"https://orcid.org/0000-0001-9199-0502"},"institutions":[{"id":"https://openalex.org/I46482218","display_name":"Anqing Normal University","ror":"https://ror.org/0127ytz78","country_code":"CN","type":"education","lineage":["https://openalex.org/I46482218"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wen-Tao Cheng","raw_affiliation_strings":["School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China"],"raw_orcid":"https://orcid.org/0000-0001-9199-0502","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China","institution_ids":["https://openalex.org/I46482218"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002429410","display_name":"Wenhui Zhang","orcid":"https://orcid.org/0000-0002-6202-8311"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen-Hui Zhang","raw_affiliation_strings":["School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China"],"raw_orcid":"https://orcid.org/0000-0002-6202-8311","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053365480","display_name":"Pei-Xin Ye","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pei-Xin Ye","raw_affiliation_strings":["School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082203192"],"corresponding_institution_ids":["https://openalex.org/I46482218"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":1.0973,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78714908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"12","issue":"1","first_page":"5","last_page":"5"},"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/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":1.0,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9671000242233276,"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"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9589999914169312,"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/modulus-of-continuity","display_name":"Modulus of continuity","score":0.770567774772644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7664647102355957},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6630698442459106},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.6614905595779419},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6091575026512146},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5281655192375183},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5001721382141113},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4800054430961609},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.4518633484840393},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44694727659225464},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38012662529945374},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06361058354377747}],"concepts":[{"id":"https://openalex.org/C3098717","wikidata":"https://www.wikidata.org/wiki/Q1144872","display_name":"Modulus of continuity","level":3,"score":0.770567774772644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7664647102355957},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6630698442459106},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.6614905595779419},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6091575026512146},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5281655192375183},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5001721382141113},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4800054430961609},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.4518633484840393},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44694727659225464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38012662529945374},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06361058354377747},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12010005","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010005","pdf_url":"https://www.mdpi.com/2075-1680/12/1/5/pdf?version=1673509809","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1afb44a7c55846dd9771df96ce799d64","is_oa":false,"landing_page_url":"https://doaj.org/article/1afb44a7c55846dd9771df96ce799d64","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 1, p 5 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/1/5/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12010005","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Axioms; Volume 12; Issue 1; Pages: 5","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12010005","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010005","pdf_url":"https://www.mdpi.com/2075-1680/12/1/5/pdf?version=1673509809","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4994585726","display_name":null,"funder_award_id":"AHSKYG2017D153","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6176718377","display_name":null,"funder_award_id":"1908085QA29","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6660522521","display_name":null,"funder_award_id":"11626031","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6665482314","display_name":null,"funder_award_id":"KJ2019A0572","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G869210956","display_name":null,"funder_award_id":"KJ2021A0648","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312186348.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1488909131","https://openalex.org/W1976589701","https://openalex.org/W2036759374","https://openalex.org/W2571446777","https://openalex.org/W2790956659","https://openalex.org/W2968555697","https://openalex.org/W3041153171","https://openalex.org/W3043700844","https://openalex.org/W3116231916","https://openalex.org/W3153187672","https://openalex.org/W3154251714","https://openalex.org/W3211632972","https://openalex.org/W3216858105","https://openalex.org/W4205354563","https://openalex.org/W4213359746","https://openalex.org/W4281727176","https://openalex.org/W4286373275"],"related_works":["https://openalex.org/W2389758888","https://openalex.org/W2443038096","https://openalex.org/W1485170658","https://openalex.org/W4287900330","https://openalex.org/W2592785930","https://openalex.org/W3041221121","https://openalex.org/W2501746113","https://openalex.org/W2040086252","https://openalex.org/W3003264596","https://openalex.org/W2057115809"],"abstract_inverted_index":{"We":[0],"construct":[1],"the":[2,15,25,35,45,61],"blending-type":[3],"modified":[4],"Bernstein\u2013Durrmeyer":[5],"operators":[6,63],"and":[7,27,40],"investigate":[8],"their":[9],"approximation":[10,29,66],"properties.":[11,67],"First,":[12],"we":[13,43],"derive":[14,44],"Voronovskaya-type":[16],"asymptotic":[17],"theorem":[18],"for":[19,49],"this":[20],"type":[21],"of":[22,38,47,54],"operator.":[23],"Then,":[24],"local":[26],"global":[28],"theorems":[30],"are":[31],"obtained":[32],"by":[33],"using":[34],"classical":[36],"modulus":[37],"continuity":[39],"K-functional.":[41],"Finally,":[42],"rate":[46],"convergence":[48],"functions":[50],"with":[51],"a":[52],"derivative":[53],"bounded":[55],"variation.":[56],"The":[57],"results":[58],"show":[59],"that":[60],"new":[62],"have":[64],"good":[65]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2023-01-04T00:00:00"}