{"id":"https://openalex.org/W7128596240","doi":"https://doi.org/10.3390/axioms15020130","title":"Bounds for the Second Hankel Determinant and Its Inverse in Specific Function Classes","display_name":"Bounds for the Second Hankel Determinant and Its Inverse in Specific Function Classes","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128596240","doi":"https://doi.org/10.3390/axioms15020130"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15020130","doi":"https://doi.org/10.3390/axioms15020130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020130","pdf_url":"https://www.mdpi.com/2075-1680/15/2/130/pdf","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,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/15/2/130/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058133892","display_name":"Trailokya Panigrahi","orcid":"https://orcid.org/0000-0001-7289-9578","observed_orcids":["https://orcid.org/0000-0001-7289-9578"]},"institutions":[{"id":"https://openalex.org/I4405283231","display_name":"Institute of Mathematics and Applications, Bhubaneswar","ror":"https://ror.org/019kvq885","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405283231"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Trailokya Panigrahi","raw_affiliation_strings":["Institute of Mathematics and Applications, Andharua, Bhubaneswar 751029, Odisha, India"],"raw_orcid":"https://orcid.org/0000-0001-7289-9578","affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Applications, Andharua, Bhubaneswar 751029, Odisha, India","institution_ids":["https://openalex.org/I4405283231"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085772420","display_name":"Teodor Bulboac\u0103","orcid":"https://orcid.org/0000-0001-8026-218X","observed_orcids":["https://orcid.org/0000-0001-8026-218X"]},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Teodor Bulboac\u0103","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Research Center of Applied Analysis, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0001-8026-218X","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Research Center of Applied Analysis, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5120143905","display_name":"Shiba Prasad Dhal","orcid":"https://orcid.org/0009-0002-4365-5499","observed_orcids":["https://orcid.org/0009-0002-4365-5499"]},"institutions":[{"id":"https://openalex.org/I4405283231","display_name":"Institute of Mathematics and Applications, Bhubaneswar","ror":"https://ror.org/019kvq885","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405283231"]},{"id":"https://openalex.org/I70699430","display_name":"Utkal University","ror":"https://ror.org/0034eez47","country_code":"IN","type":"education","lineage":["https://openalex.org/I70699430"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shiba Prasad Dhal","raw_affiliation_strings":["Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar 751004, Odisha, India","Institute of Mathematics and Applications, Andharua, Bhubaneswar 751029, Odisha, India"],"raw_orcid":"https://orcid.org/0009-0002-4365-5499","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar 751004, Odisha, India","institution_ids":["https://openalex.org/I70699430"]},{"raw_affiliation_string":"Institute of Mathematics and Applications, Andharua, Bhubaneswar 751029, Odisha, India","institution_ids":["https://openalex.org/I4405283231"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":1.9662,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77081122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"2","first_page":"130","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":1.0,"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":1.0,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.0,"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":0.0,"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/second-hankel-determinant","display_name":"second Hankel determinant","score":0.9620000123977661},{"id":"https://openalex.org/keywords/inverse-functions","display_name":"inverse functions","score":0.5379999876022339},{"id":"https://openalex.org/keywords/q-calculus","display_name":"q-calculus","score":0.7070000171661377},{"id":"https://openalex.org/keywords/subordination","display_name":"subordination","score":0.800000011920929},{"id":"https://openalex.org/keywords/analytic-functions","display_name":"analytic functions","score":0.7390000224113464},{"id":"https://openalex.org/keywords/univalent-functions","display_name":"univalent functions","score":0.8230000138282776},{"id":"https://openalex.org/keywords/fekete-szego-functional","display_name":"Fekete-Szeg\u00f6 functional","score":0.890999972820282},{"id":"https://openalex.org/keywords/initial-coefficients","display_name":"initial coefficients","score":0.8690000176429749},{"id":"https://openalex.org/keywords/geometric-function-theory","display_name":"geometric function theory","score":0.777999997138977},{"id":"https://openalex.org/keywords/coefficient-estimates","display_name":"coefficient estimates","score":0.37299999594688416}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8248999714851379},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6697999835014343},{"id":"https://openalex.org/C140528856","wikidata":"https://www.wikidata.org/wiki/Q191884","display_name":"Inverse function","level":3,"score":0.6471999883651733},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6118000149726868},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4675999879837036},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44769999384880066},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43299999833106995},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.36739999055862427},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C76134657","wikidata":"https://www.wikidata.org/wiki/Q370634","display_name":"Generalized inverse","level":3,"score":0.3499000072479248},{"id":"https://openalex.org/C2776194381","wikidata":"https://www.wikidata.org/wiki/Q3965271","display_name":"Subclass","level":3,"score":0.33309999108314514},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32199999690055847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3154999911785126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31450000405311584},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C39292890","wikidata":"https://www.wikidata.org/wiki/Q864589","display_name":"Schwarzian derivative","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms15020130","doi":"https://doi.org/10.3390/axioms15020130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020130","pdf_url":"https://www.mdpi.com/2075-1680/15/2/130/pdf","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,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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:fa6d3d72b6b446caae26e406ea78ddf7","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/fa6d3d72b6b446caae26e406ea78ddf7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 15, Iss 2, p 130 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms15020130","doi":"https://doi.org/10.3390/axioms15020130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020130","pdf_url":"https://www.mdpi.com/2075-1680/15/2/130/pdf","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,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128596240.pdf","grobid_xml":"https://content.openalex.org/works/W7128596240.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W116606405","https://openalex.org/W828682309","https://openalex.org/W1805821616","https://openalex.org/W2011687176","https://openalex.org/W2011690209","https://openalex.org/W2031275989","https://openalex.org/W2040269608","https://openalex.org/W2074741432","https://openalex.org/W2088918788","https://openalex.org/W2172520433","https://openalex.org/W2562512100","https://openalex.org/W3026404255","https://openalex.org/W4293058426","https://openalex.org/W4306701634","https://openalex.org/W4323854620","https://openalex.org/W4392201465"],"related_works":["https://openalex.org/W4403147775","https://openalex.org/W4391546576","https://openalex.org/W4296632572","https://openalex.org/W4366420012","https://openalex.org/W3143807560","https://openalex.org/W4417262478","https://openalex.org/W7162135303","https://openalex.org/W4410782673","https://openalex.org/W7172267644","https://openalex.org/W2996832741"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,114],"newly":[4],"defined":[5],"subclass":[6],"of":[7,25,38,43,48,56,64,78,84,101,105,113],"analytic":[8],"functions":[9],"and":[10,28,60,82,116],"explores":[11],"several":[12],"significant":[13],"properties":[14],"within":[15],"the":[16,23,26,29,39,44,54,57,65,73,76,89,99,102,106,109,117,125],"class,":[17],"which":[18],"use":[19],"for":[20,68,120],"their":[21,92],"definitions":[22],"q-analogues":[24],"derivative":[27],"subordinations.":[30],"Thus,":[31],"we":[32,97],"tried":[33],"to":[34],"connect":[35],"different":[36],"notions":[37],"q-calculus":[40],"with":[41],"those":[42,83],"Geometric":[45],"Function":[46],"Theory":[47],"one":[49],"variable":[50],"function.":[51],"We":[52,71],"identify":[53],"bounds":[55,63],"initial":[58],"coefficients":[59,77],"found":[61],"upper":[62],"Fekete\u2013Szeg\u0151":[66],"functional":[67],"these":[69],"classes.":[70],"investigate":[72],"relationship":[74],"between":[75,91,108],"an":[79,133],"univalent":[80],"function":[81,115],"its":[85,121],"inverse":[86],"by":[87,128],"examining":[88],"difference":[90,107],"second":[93,110],"Hankel":[94,111],"determinants.":[95],"Furthermore,":[96],"analyze":[98],"behavior":[100],"quantity":[103],"module":[104],"determinant":[112,119],"same":[118],"inverse.":[122],"To":[123],"improve":[124],"obtained":[126],"results":[127],"finding":[129],"sharp":[130],"estimations":[131],"remains":[132],"interesting":[134],"open":[135],"question.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-02-11T00:00:00"}