{"id":"https://openalex.org/W7219256788","doi":null,"title":"The approximation of bivariate generalized Bernstein-Durrmeyer type GBS operators","display_name":"The approximation of bivariate generalized Bernstein-Durrmeyer type GBS operators","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W7219256788"},"language":"en","primary_location":{"id":"pmh:oai:ojs.www.simadp.com:article/83","doi":null,"is_oa":true,"landing_page_url":"https://www.simadp.com/index/article/view/83","pdf_url":null,"source":{"id":"https://openalex.org/S7407067588","display_name":"International Journal of Maps in Mathematics","issn_l":"2636-7467","issn":["2636-7467"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2636-7467","raw_type":"info:eu-repo/semantics/article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.simadp.com/index/article/view/83","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024194453","display_name":"Ecem Acar","orcid":"https://orcid.org/0000-0002-2517-5849","observed_orcids":["https://orcid.org/0000-0002-2517-5849"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Acar, Ecem","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048391143","display_name":"Ayd\u0131n \u0130zgi","orcid":"https://orcid.org/0000-0003-3715-8621","observed_orcids":["https://orcid.org/0000-0003-3715-8621"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u0130zgi, Ayd\u0131n","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0,"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/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/convergence-rate","display_name":"convergence rate","score":0.7860000133514404},{"id":"https://openalex.org/keywords/modulus-of-continuity","display_name":"modulus of continuity","score":0.7260000109672546},{"id":"https://openalex.org/keywords/differential-operators","display_name":"differential operators","score":0.35499998927116394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8300999999046326},{"id":"https://openalex.org/C3098717","wikidata":"https://www.wikidata.org/wiki/Q1144872","display_name":"Modulus of continuity","level":3,"score":0.745199978351593},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.6402999758720398},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5673999786376953},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5544000267982483},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.5422999858856201},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43639999628067017},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.39890000224113464},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.36959999799728394},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3555000126361847},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34630000591278076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34549999237060547},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32089999318122864},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C193769641","wikidata":"https://www.wikidata.org/wiki/Q7496252","display_name":"Shift theorem","level":5,"score":0.2971000075340271},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.2782999873161316},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:ojs.www.simadp.com:article/83","doi":null,"is_oa":true,"landing_page_url":"https://www.simadp.com/index/article/view/83","pdf_url":null,"source":{"id":"https://openalex.org/S7407067588","display_name":"International Journal of Maps in Mathematics","issn_l":"2636-7467","issn":["2636-7467"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2636-7467","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ojs.www.simadp.com:article/83","doi":null,"is_oa":true,"landing_page_url":"https://www.simadp.com/index/article/view/83","pdf_url":null,"source":{"id":"https://openalex.org/S7407067588","display_name":"International Journal of Maps in Mathematics","issn_l":"2636-7467","issn":["2636-7467"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2636-7467","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3216641417","https://openalex.org/W2793246691","https://openalex.org/W4226128629","https://openalex.org/W4286373668","https://openalex.org/W2885301845","https://openalex.org/W2914436596","https://openalex.org/W2789953038","https://openalex.org/W3106656979","https://openalex.org/W2907735343","https://openalex.org/W3158221878"],"abstract_inverted_index":{"In":[0],"the":[1,6,21,44,85,92,101,120,123],"present":[2],"paper,":[3],"we":[4,65,110],"introduce":[5,66],"generalized":[7],"Bernstein-Durrmeyer":[8,67],"type":[9,50,68],"operators":[10,18,39,61,98,124],"and":[11,55,106],"obtain":[12,91],"some":[13,56,114,126],"approximation":[14,95],"properties":[15,58],"of":[16,23,26,35,37,46,59,76,87,94,104,122],"these":[17,38,60,97],"studied":[19,54],"in":[20,117],"space":[22,86],"continuous":[24,78,88],"functions":[25,79],"two":[27],"variables":[28],"on":[29],"a":[30],"compact":[31],"set.":[32],"The":[33],"rate":[34],"convergence":[36,121],"are":[40,53,62],"given":[41],"by":[42,74,99,113],"using":[43,100],"modulus":[45,103],"continuity.":[47],"A":[48],"Voronovskaya":[49],"asymptotic":[51],"theorem":[52],"differential":[57],"proved.":[63],"Further,":[64],"GBS":[69],"(Generalized":[70],"Boolean":[71],"Sum)":[72],"operator":[73],"means":[75],"B\u00f6gel":[77],"which":[80],"is":[81],"more":[82],"extensive":[83],"than":[84],"functions.":[89,127],"We":[90],"degree":[93],"for":[96,119],"mixed":[102,107],"smoothness":[105],"K-functional.":[108],"Finally,":[109],"show":[111],"comparisons":[112],"illustrative":[115],"graphics":[116],"Maple":[118],"to":[125]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2026-10-04T00:00:00"}