{"id":"https://openalex.org/W4303685535","doi":"https://doi.org/10.3390/axioms11100537","title":"Some Probabilistic Generalizations of the Cheney\u2013Sharma and Bernstein Approximation Operators","display_name":"Some Probabilistic Generalizations of the Cheney\u2013Sharma and Bernstein Approximation Operators","publication_year":2022,"publication_date":"2022-10-08","ids":{"openalex":"https://openalex.org/W4303685535","doi":"https://doi.org/10.3390/axioms11100537"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11100537","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100537","pdf_url":"https://www.mdpi.com/2075-1680/11/10/537/pdf?version=1666751518","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/2075-1680/11/10/537/pdf?version=1666751518","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082319607","display_name":"S. H. Ong","orcid":"https://orcid.org/0000-0002-4288-7637"},"institutions":[{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]},{"id":"https://openalex.org/I55285296","display_name":"UCSI University","ror":"https://ror.org/019787q29","country_code":"MY","type":"education","lineage":["https://openalex.org/I55285296"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Seng Huat Ong","raw_affiliation_strings":["Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia","Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia"],"affiliations":[{"raw_affiliation_string":"Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia","institution_ids":["https://openalex.org/I55285296"]},{"raw_affiliation_string":"Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia","institution_ids":["https://openalex.org/I33849332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013074718","display_name":"Choung Min Ng","orcid":"https://orcid.org/0000-0003-0157-2732"},"institutions":[{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Choung Min Ng","raw_affiliation_strings":["Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia","institution_ids":["https://openalex.org/I33849332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058200738","display_name":"Hong Keat Yap","orcid":"https://orcid.org/0000-0003-3350-3993"},"institutions":[{"id":"https://openalex.org/I931681460","display_name":"Universiti Tunku Abdul Rahman","ror":"https://ror.org/050pq4m56","country_code":"MY","type":"education","lineage":["https://openalex.org/I931681460"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Hong Keat Yap","raw_affiliation_strings":["Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Kajang 43000, Malaysia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Kajang 43000, Malaysia","institution_ids":["https://openalex.org/I931681460"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079512627","display_name":"H. M. Srivastava","orcid":"https://orcid.org/0000-0002-9277-8092"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]},{"id":"https://openalex.org/I87490745","display_name":"Azerbaijan University","ror":"https://ror.org/00g1psz15","country_code":"AZ","type":"education","lineage":["https://openalex.org/I87490745"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]}],"countries":["AZ","CA","IT","TW"],"is_corresponding":false,"raw_author_name":"Hari Mohan Srivastava","raw_affiliation_strings":["Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan","Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan","institution_ids":["https://openalex.org/I87490745"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I4210126829","https://openalex.org/I184693016"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082319607"],"corresponding_institution_ids":["https://openalex.org/I33849332","https://openalex.org/I55285296"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.2321,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.80650253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"10","first_page":"537","last_page":"537"},"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9498000144958496,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.920199990272522,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.8305993676185608},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7403162717819214},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6790223717689514},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6515752673149109},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.6424381732940674},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5858330130577087},{"id":"https://openalex.org/keywords/baskakov-operator","display_name":"Baskakov operator","score":0.4258325695991516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4203651249408722},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.33902791142463684},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.3158332407474518},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3153102695941925},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15580132603645325},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11562079191207886},{"id":"https://openalex.org/keywords/microlocal-analysis","display_name":"Microlocal analysis","score":0.11059743165969849},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07292136549949646},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.0663762092590332}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.8305993676185608},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7403162717819214},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6790223717689514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6515752673149109},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.6424381732940674},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5858330130577087},{"id":"https://openalex.org/C101346110","wikidata":"https://www.wikidata.org/wiki/Q4867603","display_name":"Baskakov operator","level":5,"score":0.4258325695991516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4203651249408722},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33902791142463684},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3158332407474518},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3153102695941925},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15580132603645325},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11562079191207886},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.11059743165969849},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07292136549949646},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.0663762092590332},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms11100537","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100537","pdf_url":"https://www.mdpi.com/2075-1680/11/10/537/pdf?version=1666751518","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:cb1c6aa1de984703bdd5f7ebce8918e1","is_oa":true,"landing_page_url":"https://doaj.org/article/cb1c6aa1de984703bdd5f7ebce8918e1","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 10, p 537 (2022)","raw_type":"article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/14420","is_oa":false,"landing_page_url":"http://hdl.handle.net/1828/14420","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/10/537/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11100537","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 11; Issue 10; Pages: 537","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11100537","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100537","pdf_url":"https://www.mdpi.com/2075-1680/11/10/537/pdf?version=1666751518","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/G2431155031","display_name":null,"funder_award_id":"FRGS/1/2020/STG06/SYUC/02/1","funder_id":"https://openalex.org/F4320321709","funder_display_name":"Ministry of Higher Education, Malaysia"}],"funders":[{"id":"https://openalex.org/F4320321709","display_name":"Ministry of Higher Education, Malaysia","ror":"https://ror.org/05mcs2t73"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4303685535.pdf","grobid_xml":"https://content.openalex.org/works/W4303685535.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W2003656995","https://openalex.org/W2087907981","https://openalex.org/W2099138610","https://openalex.org/W2146368895","https://openalex.org/W2313968760","https://openalex.org/W2325877082","https://openalex.org/W2567369073","https://openalex.org/W2581852911","https://openalex.org/W2735958099","https://openalex.org/W2954697388","https://openalex.org/W2980084962","https://openalex.org/W3167731107","https://openalex.org/W3200326139","https://openalex.org/W4229365473","https://openalex.org/W6733009603","https://openalex.org/W6811001287"],"related_works":["https://openalex.org/W2391096262","https://openalex.org/W2952252896","https://openalex.org/W4406938385","https://openalex.org/W2367161241","https://openalex.org/W2949793012","https://openalex.org/W2379115614","https://openalex.org/W339147017","https://openalex.org/W2024801457","https://openalex.org/W2155220805","https://openalex.org/W2963059954"],"abstract_inverted_index":{"The":[0,34],"objective":[1],"of":[2,11,25,37],"this":[3],"paper":[4],"is":[5,41,44,51],"to":[6],"give":[7],"some":[8],"probabilistic":[9,22],"derivations":[10],"the":[12,26,38,48,52],"Cheney,":[13,27],"Sharma,":[14,28],"and":[15,29],"Bernstein":[16,30,39],"approximation":[17],"operators.":[18],"Motivated":[19],"by":[20,56],"these":[21],"derivations,":[23],"generalizations":[24],"operators":[31],"are":[32],"defined.":[33],"convergence":[35],"property":[36],"generalization":[40],"established.":[42],"It":[43],"also":[45],"shown":[46],"that":[47],"Cheney\u2013Sharma":[49],"operator":[50,54],"Sz\u00e1sz\u2013Mirakyan":[53],"averaged":[55],"a":[57],"certain":[58],"probability":[59],"distribution.":[60]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
