{"id":"https://openalex.org/W7223874564","doi":"https://doi.org/10.48550/arxiv.2610.33031","title":"Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order $\u03b1$ and Quasi-Convex Mappings of Type $B$ in Complex Banach Spaces","display_name":"Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order $\u03b1$ and Quasi-Convex Mappings of Type $B$ in Complex Banach Spaces","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7223874564","doi":"https://doi.org/10.48550/arxiv.2610.33031"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33031","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33031","pdf_url":"https://arxiv.org/pdf/2610.33031","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.33031","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101626134","display_name":"Sujoy Majumder","orcid":"https://orcid.org/0000-0001-7019-3694","observed_orcids":["https://orcid.org/0000-0001-7019-3694"]},"institutions":[{"id":"https://openalex.org/I275778967","display_name":"Raiganj University","ror":"https://ror.org/00bneyt76","country_code":"IN","type":"education","lineage":["https://openalex.org/I275778967"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Majumder, Sujoy","raw_affiliation_strings":["Department of Mathematics , Raiganj University , Raiganj , West Bengal- 733134 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Raiganj University , Raiganj , West Bengal- 733134 , India","institution_ids":["https://openalex.org/I275778967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102010921","display_name":"Abhijit Banerjee","orcid":"https://orcid.org/0000-0002-6160-7506","observed_orcids":["https://orcid.org/0000-0002-6160-7506"]},"institutions":[{"id":"https://openalex.org/I77501641","display_name":"University of Kalyani","ror":"https://ror.org/03v783k16","country_code":"IN","type":"education","lineage":["https://openalex.org/I77501641"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Banerjee, Abhijit","raw_affiliation_strings":["Abhijit Banerjee , Department of Mathematics , University of Kalyani , West Bengal 741235 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abhijit Banerjee , Department of Mathematics , University of Kalyani , West Bengal 741235 , India","institution_ids":["https://openalex.org/I77501641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103128424","display_name":"S. Panja","orcid":"https://orcid.org/0009-0006-6159-5599","observed_orcids":["https://orcid.org/0009-0006-6159-5599"]},"institutions":[{"id":"https://openalex.org/I77501641","display_name":"University of Kalyani","ror":"https://ror.org/03v783k16","country_code":"IN","type":"education","lineage":["https://openalex.org/I77501641"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Panja, Shantanu","raw_affiliation_strings":["Department of Mathematics , University of Kalyani , West Bengal 741235 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Kalyani , West Bengal 741235 , India","institution_ids":["https://openalex.org/I77501641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111427283","display_name":"Debabrata Pramanik","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I275778967","display_name":"Raiganj University","ror":"https://ror.org/00bneyt76","country_code":"IN","type":"education","lineage":["https://openalex.org/I275778967"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pramanik, Debabrata","raw_affiliation_strings":["Debabrata Pramanik , Department of Mathematics , Raiganj University , Raiganj , West Bengal- 733134 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Debabrata Pramanik , Department of Mathematics , Raiganj University , Raiganj , West Bengal- 733134 , India","institution_ids":["https://openalex.org/I275778967"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.0003000000142492354,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":9.999999747378752e-05,"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/hankel-determinants","display_name":"Hankel determinants","score":0.9259999990463257},{"id":"https://openalex.org/keywords/unit-ball","display_name":"unit ball","score":0.7860000133514404},{"id":"https://openalex.org/keywords/unit-polydisk","display_name":"unit polydisc","score":0.9959999918937683},{"id":"https://openalex.org/keywords/coefficient-estimates","display_name":"coefficient estimates","score":0.765999972820282},{"id":"https://openalex.org/keywords/geometric-function-theory","display_name":"geometric function theory","score":0.7390000224113464}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7942000031471252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.777400016784668},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.7330999970436096},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6984000205993652},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.5795000195503235},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5676000118255615},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5432999730110168},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5329999923706055},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4392000138759613},{"id":"https://openalex.org/C42178598","wikidata":"https://www.wikidata.org/wiki/Q1585233","display_name":"Hardy space","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.39320001006126404},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.37720000743865967},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3614000082015991},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32260000705718994},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.28299999237060547},{"id":"https://openalex.org/C107264478","wikidata":"https://www.wikidata.org/wiki/Q3058183","display_name":"Bergman space","level":3,"score":0.2621000111103058},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.33031","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33031","pdf_url":"https://arxiv.org/pdf/2610.33031","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.33031","doi":"https://doi.org/10.48550/arxiv.2610.33031","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33031","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.33031","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33031","pdf_url":"https://arxiv.org/pdf/2610.33031","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223874564.pdf","grobid_xml":"https://content.openalex.org/works/W7223874564.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7169833745","https://openalex.org/W4410602476","https://openalex.org/W7202202775","https://openalex.org/W7116769858","https://openalex.org/W7222417870","https://openalex.org/W7168400299","https://openalex.org/W7167454473","https://openalex.org/W7221799237","https://openalex.org/W3094575246","https://openalex.org/W2626471149"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"and":[5,48,80,99,110],"investigate":[6],"a":[7,44,76],"parameterized":[8],"Hankel-type":[9],"functional":[10],"$$H_{2,2}^\u03bc(f)=\u03bca_2a_4-a_3^2,\\qquad":[11],"\u03bc\\in[0,1],":[12],"$$":[13],"which":[14],"reduces":[15],"to":[16,115],"the":[17,31,40,50,63,72,82,91,95,101],"classical":[18,96],"second-order":[19],"Hankel":[20,97],"determinant":[21,98],"$H_{2,2}(f)$":[22],"when":[23],"$\u03bc=1$.":[24],"We":[25,56],"obtain":[26],"estimates":[27,59,93],"for":[28,60,94],"$H_{2,2}^\u03bc(f)$":[29,61],"over":[30,62],"class":[32,64],"of":[33,36,43,65,68,75,105],"starlike":[34],"mappings":[35,67],"order":[37],"$\u03b1$":[38],"on":[39,49,71,81],"unit":[41,51,73,83],"ball":[42,74],"complex":[45,77],"Banach":[46,78],"space":[47,79],"polydisk":[52,84],"$\\mathbb{U}^n$":[53],"in":[54],"$\\mathbb{C}^n$.":[55],"also":[57],"establish":[58],"quasi-convex":[66],"type":[69],"$B$":[70],"$\\mathbb{U}^n$.":[85],"For":[86],"$\u03bc=1$,":[87],"our":[88],"results":[89,104],"recover":[90],"corresponding":[92],"extend":[100],"known":[102],"one-dimensional":[103],"Cho":[106],"et":[107,112],"al.":[108,113],"\\cite{Cho-2018}":[109],"Thomas":[111],"\\cite{Thomas-Tuneski}":[114],"higher-dimensional":[116],"settings.":[117]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-28T00:00:00"}