{"id":"https://openalex.org/W4410864817","doi":"https://doi.org/10.3390/axioms14060418","title":"Sz\u00e1sz\u2013Beta Operators Linking Frobenius\u2013Euler\u2013Simsek-Type Polynomials","display_name":"Sz\u00e1sz\u2013Beta Operators Linking Frobenius\u2013Euler\u2013Simsek-Type Polynomials","publication_year":2025,"publication_date":"2025-05-29","ids":{"openalex":"https://openalex.org/W4410864817","doi":"https://doi.org/10.3390/axioms14060418"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14060418","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060418","pdf_url":null,"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://doi.org/10.3390/axioms14060418","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060715839","display_name":"Nadeem Rao","orcid":"https://orcid.org/0000-0002-5681-9563"},"institutions":[{"id":"https://openalex.org/I101407740","display_name":"Chandigarh University","ror":"https://ror.org/05t4pvx35","country_code":"IN","type":"education","lineage":["https://openalex.org/I101407740"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Nadeem Rao","raw_affiliation_strings":["Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali 140413, Punjab, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali 140413, Punjab, India","institution_ids":["https://openalex.org/I101407740"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102013924","display_name":"Mohammad Farid","orcid":"https://orcid.org/0000-0002-9713-3509"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohammad Farid","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008416810","display_name":"Shivani Bansal","orcid":"https://orcid.org/0000-0002-7805-4362"},"institutions":[{"id":"https://openalex.org/I101407740","display_name":"Chandigarh University","ror":"https://ror.org/05t4pvx35","country_code":"IN","type":"education","lineage":["https://openalex.org/I101407740"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shivani Bansal","raw_affiliation_strings":["Department of Mathematics, University Institute of Sciences, Chandigarh University, Mohali 140413, Punjab, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Institute of Sciences, Chandigarh University, Mohali 140413, Punjab, India","institution_ids":["https://openalex.org/I101407740"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060715839"],"corresponding_institution_ids":["https://openalex.org/I101407740"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.8227,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89704596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"14","issue":"6","first_page":"418","last_page":"418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9994000196456909,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/type","display_name":"Type (biology)","score":0.6812620162963867},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5915160775184631},{"id":"https://openalex.org/keywords/beta","display_name":"BETA (programming language)","score":0.5861465334892273},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5655021667480469},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4710155725479126},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19626551866531372},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18427830934524536},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06594988703727722},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.033435940742492676}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6812620162963867},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5915160775184631},{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.5861465334892273},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5655021667480469},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4710155725479126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19626551866531372},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18427830934524536},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06594988703727722},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.033435940742492676},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14060418","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060418","pdf_url":null,"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:a15b37cb9b6d4e3c94072b18a65ee2fe","is_oa":true,"landing_page_url":"https://doaj.org/article/a15b37cb9b6d4e3c94072b18a65ee2fe","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 14, Iss 6, p 418 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14060418","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060418","pdf_url":null,"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/G2186466424","display_name":null,"funder_award_id":"QU-APC-2025","funder_id":"https://openalex.org/F4320324403","funder_display_name":"Qassim University"}],"funders":[{"id":"https://openalex.org/F4320324403","display_name":"Qassim University","ror":"https://ror.org/01wsfe280"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1972847999","https://openalex.org/W1976589701","https://openalex.org/W1989203263","https://openalex.org/W2021065822","https://openalex.org/W2094043756","https://openalex.org/W2602976799","https://openalex.org/W2746937177","https://openalex.org/W2791404527","https://openalex.org/W2918274972","https://openalex.org/W2950122019","https://openalex.org/W3008979912","https://openalex.org/W3100210567","https://openalex.org/W3120336953","https://openalex.org/W3165369640","https://openalex.org/W4205354563","https://openalex.org/W4281684643","https://openalex.org/W4404584502","https://openalex.org/W4405726495","https://openalex.org/W4408925398","https://openalex.org/W4409806664","https://openalex.org/W6674156184","https://openalex.org/W6757190102","https://openalex.org/W6920403970"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"This":[0],"manuscript":[1],"associates":[2],"with":[3,55],"a":[4,15],"study":[5],"of":[6,18,41,51,58,73,75,77,116],"Frobenius\u2013Euler\u2013Simsek-type":[7,23],"Polynomials.":[8],"In":[9,95],"this":[10],"research":[11],"work,":[12],"we":[13,99,120],"construct":[14],"new":[16],"sequence":[17],"Sz\u00e1sz\u2013Beta":[19],"type":[20,65,84,90],"operators":[21],"via":[22],"Polynomials":[24],"to":[25],"discuss":[26],"approximation":[27,69,102,106],"properties":[28],"for":[29],"the":[30,56,59,63,87,96,112,117,127],"Lebesgue":[31],"integrable":[32],"functions,":[33],"i.e.,":[34],"Lp[0,\u221e),":[35],"1\u2264p<\u221e.":[36],"Furthermore,":[37],"estimates":[38],"in":[39,71],"view":[40],"test":[42],"functions":[43,92],"and":[44,62,79,86,104,114,125],"central":[45],"moments":[46],"are":[47,93,108],"studied.":[48],"Next,":[49],"rate":[50],"convergence":[52],"is":[53],"discussed":[54],"aid":[57],"Korovkin":[60],"theorem":[61],"Voronovskaja":[64],"theorem.":[66],"Moreover,":[67],"direct":[68],"results":[70,128],"terms":[72],"modulus":[74],"continuity":[76],"first-":[78],"second-order,":[80],"Peetre\u2019s":[81],"K-functional,":[82],"Lipschitz":[83,89],"space,":[85],"rth-order":[88],"maximal":[91],"investigated.":[94],"subsequent":[97],"section,":[98],"present":[100,121],"weighted":[101],"results,":[103],"statistical":[105],"theorems":[107],"discussed.":[109],"To":[110],"demonstrate":[111],"effectiveness":[113],"applicability":[115],"proposed":[118],"operators,":[119],"several":[122],"illustrative":[123],"examples":[124],"visualize":[126],"graphically.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}