{"id":"https://openalex.org/W4360614575","doi":"https://doi.org/10.31801/cfsuasmas.1089790","title":"Some refinements of Berezin number inequalities via convex functions","display_name":"Some refinements of Berezin number inequalities via convex functions","publication_year":2023,"publication_date":"2023-03-23","ids":{"openalex":"https://openalex.org/W4360614575","doi":"https://doi.org/10.31801/cfsuasmas.1089790"},"language":"en","primary_location":{"id":"doi:10.31801/cfsuasmas.1089790","doi":"https://doi.org/10.31801/cfsuasmas.1089790","is_oa":true,"landing_page_url":"https://doi.org/10.31801/cfsuasmas.1089790","pdf_url":"https://dergipark.org.tr/en/download/article-file/2317713","source":{"id":"https://openalex.org/S4210232279","display_name":"Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics","issn_l":"1303-5991","issn":["1303-5991"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-d","poland-20","russia-white-list-3","tr-dizin"],"host_organization":"https://openalex.org/P4310318375","host_organization_name":"Ankara University","host_organization_lineage":["https://openalex.org/P4310318375"],"host_organization_lineage_names":["Ankara University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dergipark.org.tr/en/download/article-file/2317713","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079855423","display_name":"Suna Saltan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I175124709","display_name":"S\u00fcleyman Demirel \u00dcniversitesi","ror":"https://ror.org/04fjtte88","country_code":"TR","type":"education","lineage":["https://openalex.org/I175124709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Suna SALTAN","raw_affiliation_strings":["SULEYMAN DEMIREL UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SULEYMAN DEMIREL UNIVERSITY","institution_ids":["https://openalex.org/I175124709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026788248","display_name":"Nazl\u0131 BASKAN","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I175124709","display_name":"S\u00fcleyman Demirel \u00dcniversitesi","ror":"https://ror.org/04fjtte88","country_code":"TR","type":"education","lineage":["https://openalex.org/I175124709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Nazl\u0131 BASKAN","raw_affiliation_strings":["SULEYMAN DEMIREL UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SULEYMAN DEMIREL UNIVERSITY","institution_ids":["https://openalex.org/I175124709"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I175124709"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"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":"72","issue":"1","first_page":"32","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9965999722480774,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9965999722480774,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.002199999988079071,"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/T10899","display_name":"Advanced Operator Algebra Research","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/berezin-number","display_name":"Berezin number","score":0.9850000143051147},{"id":"https://openalex.org/keywords/berezin-transform","display_name":"Berezin transform","score":0.9959999918937683},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"reproducing kernel Hilbert space","score":0.9850000143051147},{"id":"https://openalex.org/keywords/convex-functions","display_name":"convex functions","score":0.9210000038146973},{"id":"https://openalex.org/keywords/operator-inequalities","display_name":"operator inequalities","score":0.7960000038146973},{"id":"https://openalex.org/keywords/operator-norm","display_name":"operator norm","score":0.35600000619888306}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7013881802558899},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6101272702217102},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5744635462760925},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.46765536069869995},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4561211168766022},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.45422840118408203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4515102505683899},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4119845926761627},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3569832742214203},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.241813063621521},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20990589261054993},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10358598828315735}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.31801/cfsuasmas.1089790","doi":"https://doi.org/10.31801/cfsuasmas.1089790","is_oa":true,"landing_page_url":"https://doi.org/10.31801/cfsuasmas.1089790","pdf_url":"https://dergipark.org.tr/en/download/article-file/2317713","source":{"id":"https://openalex.org/S4210232279","display_name":"Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics","issn_l":"1303-5991","issn":["1303-5991"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-d","poland-20","russia-white-list-3","tr-dizin"],"host_organization":"https://openalex.org/P4310318375","host_organization_name":"Ankara University","host_organization_lineage":["https://openalex.org/P4310318375"],"host_organization_lineage_names":["Ankara University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics","raw_type":"journal-article"},{"id":"pmh:oai:dergipark.org.tr:article/1089790","doi":null,"is_oa":true,"landing_page_url":"https://dergipark.org.tr/tr/pub/cfsuasmas/issue/76131/1089790","pdf_url":null,"source":{"id":"https://openalex.org/S4210232279","display_name":"Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics","issn_l":"1303-5991","issn":["1303-5991"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-d","poland-20","russia-white-list-3","tr-dizin"],"host_organization":"https://openalex.org/P4310318375","host_organization_name":"Ankara University","host_organization_lineage":["https://openalex.org/P4310318375"],"host_organization_lineage_names":["Ankara University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.31801/cfsuasmas.1089790","doi":"https://doi.org/10.31801/cfsuasmas.1089790","is_oa":true,"landing_page_url":"https://doi.org/10.31801/cfsuasmas.1089790","pdf_url":"https://dergipark.org.tr/en/download/article-file/2317713","source":{"id":"https://openalex.org/S4210232279","display_name":"Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics","issn_l":"1303-5991","issn":["1303-5991"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-d","poland-20","russia-white-list-3","tr-dizin"],"host_organization":"https://openalex.org/P4310318375","host_organization_name":"Ankara University","host_organization_lineage":["https://openalex.org/P4310318375"],"host_organization_lineage_names":["Ankara University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4360614575.pdf","grobid_xml":"https://content.openalex.org/works/W4360614575.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W164846852","https://openalex.org/W1986280275","https://openalex.org/W2012886538","https://openalex.org/W2032842938","https://openalex.org/W2049710258","https://openalex.org/W2067800874","https://openalex.org/W2071898434","https://openalex.org/W2076109406","https://openalex.org/W2171690926","https://openalex.org/W2192444510","https://openalex.org/W2325330392","https://openalex.org/W2509586437","https://openalex.org/W2790783404","https://openalex.org/W2800049368","https://openalex.org/W2910795602","https://openalex.org/W2937214860","https://openalex.org/W2949462558","https://openalex.org/W2962846525","https://openalex.org/W2963479036","https://openalex.org/W2970843869","https://openalex.org/W3002764010","https://openalex.org/W3025683959","https://openalex.org/W3216174918","https://openalex.org/W4200189269","https://openalex.org/W4205349806","https://openalex.org/W4235581704","https://openalex.org/W4249104068","https://openalex.org/W4312919342"],"related_works":["https://openalex.org/W4312919342","https://openalex.org/W4398789718","https://openalex.org/W4381712818","https://openalex.org/W4285393735","https://openalex.org/W3001368110","https://openalex.org/W3156098588","https://openalex.org/W7082368461","https://openalex.org/W2795462873","https://openalex.org/W4381989614","https://openalex.org/W2800962568"],"abstract_inverted_index":{"The":[0],"Berezin":[1,6,75],"transform":[2],"$\\widetilde{A}$":[3],"and":[4,36,88],"the":[5,13,48],"number":[7,76],"of":[8,74],"an":[9],"operator":[10],"$A$":[11],"on":[12],"reproducing":[14,24],"kernel":[15,25],"Hilbert":[16],"space":[17],"over":[18],"some":[19,72],"set":[20],"$\\Omega$":[21],"with":[22],"normalized":[23],"$\\widehat{k}_{\\lambda}$":[26],"are":[27],"defined,":[28],"respectively,":[29],"by":[30],"$\\widetilde{A}(\\lambda)=\\left\\langle":[31],"{A}\\widehat{k}_{\\lambda":[32],"},\\widehat{k}_{\\lambda}\\right\\rangle":[33],",\\":[34],"\\lambda\\in\\Omega$":[35],"$\\mathrm{ber}%":[37],"(A):=\\sup_{\\lambda\\in\\Omega}\\left\\vert":[38],"\\widetilde{A}{(\\lambda)}\\right\\vert":[39],".$":[40],"A":[41],"straightforward":[42],"comparison":[43],"between":[44],"these":[45],"characteristics":[46],"yields":[47],"inequalities":[49,66,77],"$\\mathrm{ber}\\left(":[50],"A\\right)":[51,95],"\\leq\\frac{1}{2}\\left(":[52],"\\left\\Vert":[53,97],"A\\right\\Vert":[54],"_{\\mathrm{ber}}+\\left\\Vert":[55],"A^{2}\\right\\Vert":[56],"_{\\mathrm{ber}}%":[57],"^{1/2}\\right)":[58],"$.":[59],"In":[60,81],"this":[61],"paper,":[62],"we":[63,70,90],"study":[64],"further":[65],"relating":[67],"them.":[68],"Namely,":[69],"obtained":[71],"refinement":[73],"involving":[78],"convex":[79],"functions.":[80],"particular,":[82],"for":[83],"$A\\in\\mathcal{B}\\left(":[84],"\\mathcal{H}%":[85],"\\right)":[86],"$":[87],"$r\\geq1$":[89],"show":[91],"that":[92],"\\[":[93],"\\mathrm{ber}^{2r}\\left(":[94],"\\leq\\frac{1}{4}\\left(":[96],"A^{\\ast":[98],"}A+AA^{\\ast}\\right\\Vert":[99],"_{\\mathrm{ber}}^{r}+\\left\\Vert":[100],"A^{\\ast}A-AA^{\\ast":[101],"}\\right\\Vert":[102],"_{\\mathrm{ber}}^{r}\\right)":[103],"+\\frac{1}{2}\\mathrm{ber}^{r}\\left(":[104],"A^{2}\\right)":[105],".":[106],"\\]":[107]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2023-03-24T00:00:00"}