{"id":"https://openalex.org/W4320150572","doi":"https://doi.org/10.3934/mfc.2022062","title":"A new variant of the modified Bernstein-Kantorovich operators defined by \u00d6zarslan and Duman","display_name":"A new variant of the modified Bernstein-Kantorovich operators defined by \u00d6zarslan and Duman","publication_year":2023,"publication_date":"2023-01-10","ids":{"openalex":"https://openalex.org/W4320150572","doi":"https://doi.org/10.3934/mfc.2022062"},"language":"en","primary_location":{"id":"doi:10.3934/mfc.2022062","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2022062","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=63aec113aa1db67769a0fc00","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=63aec113aa1db67769a0fc00","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101483237","display_name":"Abhishek Kumar","orcid":"https://orcid.org/0000-0003-4830-1809"},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Abhishek Kumar","raw_affiliation_strings":["College University of Delhi New Delhi-110003"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College University of Delhi New Delhi-110003","institution_ids":["https://openalex.org/I110166357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101483237"],"corresponding_institution_ids":["https://openalex.org/I110166357"],"apc_list":null,"apc_paid":null,"fwci":0.5689,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65278689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"7","issue":"1","first_page":"113","last_page":"135"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9977999925613403,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/mathematics","display_name":"Mathematics","score":0.6810911893844604},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.541265606880188},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5351582169532776},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5264595150947571},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.5120232701301575},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4847981035709381},{"id":"https://openalex.org/keywords/modulus-of-continuity","display_name":"Modulus of continuity","score":0.4760603606700897},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4713320732116699},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46466103196144104},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4613935947418213},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.45342564582824707},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45259594917297363},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40590700507164},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3171221613883972},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10450392961502075}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6810911893844604},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.541265606880188},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5351582169532776},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5264595150947571},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.5120232701301575},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4847981035709381},{"id":"https://openalex.org/C3098717","wikidata":"https://www.wikidata.org/wiki/Q1144872","display_name":"Modulus of continuity","level":3,"score":0.4760603606700897},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4713320732116699},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46466103196144104},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4613935947418213},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.45342564582824707},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45259594917297363},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40590700507164},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3171221613883972},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10450392961502075},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/mfc.2022062","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2022062","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=63aec113aa1db67769a0fc00","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/mfc.2022062","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2022062","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=63aec113aa1db67769a0fc00","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4320150572.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1973629111","https://openalex.org/W1977294543","https://openalex.org/W2010150725","https://openalex.org/W2036759374","https://openalex.org/W2038698311","https://openalex.org/W2060445959","https://openalex.org/W2094043756","https://openalex.org/W2152811669","https://openalex.org/W2222445264","https://openalex.org/W2789237874","https://openalex.org/W3008761527","https://openalex.org/W3125360505","https://openalex.org/W3135109640","https://openalex.org/W3158022368","https://openalex.org/W3185934244","https://openalex.org/W3206655506","https://openalex.org/W4205125725","https://openalex.org/W4205354563","https://openalex.org/W4205546082","https://openalex.org/W4226120125","https://openalex.org/W4285305182","https://openalex.org/W4312614244"],"related_works":["https://openalex.org/W2350325755","https://openalex.org/W2356614471","https://openalex.org/W1994780266","https://openalex.org/W2299820641","https://openalex.org/W2389758888","https://openalex.org/W4288249413","https://openalex.org/W3004045233","https://openalex.org/W1485170658","https://openalex.org/W2592785930","https://openalex.org/W2501746113"],"abstract_inverted_index":{"In":[0],"the":[1,13,26,41,68,71,77,82,94,112,148,154,161,165,172],"present":[2],"article,":[3],"we":[4,92,129,158],"introduce":[5],"a":[6,138,144],"new":[7],"function":[8,27,39,149],"$":[9,11,28,30,44,57,59,117,150,152],"\\zeta":[10,29],"in":[12,40,116,122],"modified":[14,173],"Bernstein-Kantorovich":[15,174],"operators":[16,156,175],"defined":[17,176],"by":[18,98,109,137,177],"\u00d6zarslan":[19,178],"and":[20,23,58,75,105,141,157],"Duman":[21],"(http://dx.doi.org/10.1080/01630563.2015.1079219)":[22],"properties":[24,66],"of":[25,70,79,84,86,96,100,102,111,147],"is":[31,35],"define":[32],"as:":[33],"this":[34],"an":[36,64,106],"infinitely":[37],"differentiable":[38],"closed":[42],"interval":[43],"[0,":[45],"1]":[46],"\\;":[47,53],"\\text{such":[48],"that}\\;":[49],"\\zeta(0)":[50],"=":[51,55],"0,":[52],"\\zeta(1)":[54],"1":[56],"\\zeta'(\\varkappa)":[60],"$.":[61],"We":[62],"discussed":[63],"approximation":[65,107,167],"with":[67,81],"help":[69],"Bohman-Korovkin's":[72,113],"type":[73,89,114],"theorem":[74,108,115],"scrutinize":[76],"rate":[78,95],"convergence":[80,97],"aid":[83],"modulus":[85],"continuity,":[87],"Lipschitz":[88],"functions.":[90],"Furthermore,":[91],"study":[93],"means":[99],"derivatives":[101],"bounded":[103],"variation":[104],"using":[110],"\\mathcal{A}-":[118],"$Statistical":[119],"convergence.In":[120],"lastly,":[121],"order":[123],"to":[124,171],"validate":[125],"our":[126,162],"theoretical":[127],"results,":[128],"provide":[130],"some":[131],"numerical":[132],"experiments":[133],"that":[134,143,160],"are":[135],"produced":[136],"MATHEMATICA":[139],"compiler":[140],"show":[142],"careful":[145],"choice":[146],"\\zeta(\\varkappa)":[151],"for":[153],"both":[155],"see":[159],"operator":[163],"gives":[164],"better":[166],"results":[168],"as":[169],"compare":[170],"(doi.org/10.1080/01630563.2015.1079219).":[179]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-02-03T00:53:05.648605","created_date":"2025-10-10T00:00:00"}
