{"id":"https://openalex.org/W4288447652","doi":"https://doi.org/10.3390/axioms11080369","title":"Sharp Bounds for the Second Hankel Determinant of Logarithmic Coefficients for Strongly Starlike and Strongly Convex Functions","display_name":"Sharp Bounds for the Second Hankel Determinant of Logarithmic Coefficients for Strongly Starlike and Strongly Convex Functions","publication_year":2022,"publication_date":"2022-07-28","ids":{"openalex":"https://openalex.org/W4288447652","doi":"https://doi.org/10.3390/axioms11080369"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11080369","doi":"https://doi.org/10.3390/axioms11080369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11080369","pdf_url":"https://www.mdpi.com/2075-1680/11/8/369/pdf?version=1658995685","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/2075-1680/11/8/369/pdf?version=1658995685","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079344050","display_name":"Sevtap S\u00fcmer Eker","orcid":"https://orcid.org/0000-0002-2573-0726","observed_orcids":["https://orcid.org/0000-0002-2573-0726"]},"institutions":[{"id":"https://openalex.org/I123466251","display_name":"Dicle University","ror":"https://ror.org/0257dtg16","country_code":"TR","type":"education","lineage":["https://openalex.org/I123466251"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Sevtap S\u00fcmer Eker","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbak\u0131r, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-2573-0726","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbak\u0131r, Turkey","institution_ids":["https://openalex.org/I123466251"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006485747","display_name":"Bilal \u015eeker","orcid":"https://orcid.org/0000-0003-1777-8145","observed_orcids":["https://orcid.org/0000-0003-1777-8145"]},"institutions":[{"id":"https://openalex.org/I123466251","display_name":"Dicle University","ror":"https://ror.org/0257dtg16","country_code":"TR","type":"education","lineage":["https://openalex.org/I123466251"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Bilal \u015eeker","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbak\u0131r, Turkey"],"raw_orcid":"https://orcid.org/0000-0003-1777-8145","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbak\u0131r, Turkey","institution_ids":["https://openalex.org/I123466251"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052261745","display_name":"Bilal \u00c7eki\u00e7","orcid":"https://orcid.org/0000-0002-6408-0455","observed_orcids":["https://orcid.org/0000-0002-6408-0455"]},"institutions":[{"id":"https://openalex.org/I123466251","display_name":"Dicle University","ror":"https://ror.org/0257dtg16","country_code":"TR","type":"education","lineage":["https://openalex.org/I123466251"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Bilal \u00c7eki\u00e7","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbak\u0131r, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-6408-0455","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbak\u0131r, Turkey","institution_ids":["https://openalex.org/I123466251"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086092519","display_name":"Mugur Acu","orcid":"https://orcid.org/0000-0002-9333-7109","observed_orcids":["https://orcid.org/0000-0002-9333-7109"]},"institutions":[{"id":"https://openalex.org/I124121301","display_name":"Lucian Blaga University of Sibiu","ror":"https://ror.org/026gdz537","country_code":"RO","type":"education","lineage":["https://openalex.org/I124121301"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Mugur Acu","raw_affiliation_strings":["Department of Mathematics and Informatics, Faculty of Science, Lucian Blaga University of Sibiu, Street Dr. I. Ratiu 5\u20137, 550012 Sibiu, Romania"],"raw_orcid":"https://orcid.org/0000-0002-9333-7109","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Faculty of Science, Lucian Blaga University of Sibiu, Street Dr. I. Ratiu 5\u20137, 550012 Sibiu, Romania","institution_ids":["https://openalex.org/I124121301"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079344050"],"corresponding_institution_ids":["https://openalex.org/I123466251"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1675},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1675},"fwci":4.454,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.95515729,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"11","issue":"8","first_page":"369","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9994999766349792,"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":0.9994999766349792,"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/T10884","display_name":"Holomorphic and Operator Theory","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"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithmic-coefficients","display_name":"logarithmic coefficients","score":0.9649999737739563},{"id":"https://openalex.org/keywords/second-hankel-determinant","display_name":"second Hankel determinant","score":0.9470000267028809},{"id":"https://openalex.org/keywords/strongly-starlike-functions","display_name":"strongly starlike functions","score":0.9950000047683716},{"id":"https://openalex.org/keywords/strongly-convex-functions","display_name":"strongly convex functions","score":1.0},{"id":"https://openalex.org/keywords/univalent-functions","display_name":"univalent functions","score":0.9879999756813049},{"id":"https://openalex.org/keywords/taylor-coefficients","display_name":"Taylor coefficients","score":0.7080000042915344},{"id":"https://openalex.org/keywords/analytic-functions","display_name":"analytic functions","score":0.5929999947547913}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.8982683420181274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.769463300704956},{"id":"https://openalex.org/C36649600","wikidata":"https://www.wikidata.org/wiki/Q762521","display_name":"Logarithmic derivative","level":2,"score":0.7078468203544617},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5951143503189087},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5485693216323853},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4849541187286377},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47516176104545593},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4548805356025696},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.4130186140537262},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05079352855682373},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms11080369","doi":"https://doi.org/10.3390/axioms11080369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11080369","pdf_url":"https://www.mdpi.com/2075-1680/11/8/369/pdf?version=1658995685","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:9e23fa547a53435280fd076c4e865bfb","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/9e23fa547a53435280fd076c4e865bfb","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 8, p 369 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms11080369","doi":"https://doi.org/10.3390/axioms11080369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11080369","pdf_url":"https://www.mdpi.com/2075-1680/11/8/369/pdf?version=1658995685","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4288447652.pdf","grobid_xml":"https://content.openalex.org/works/W4288447652.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1985742294","https://openalex.org/W2083933580","https://openalex.org/W2110601747","https://openalex.org/W2153535232","https://openalex.org/W2256220809","https://openalex.org/W2327672688","https://openalex.org/W2795776160","https://openalex.org/W2806185077","https://openalex.org/W2810515886","https://openalex.org/W2911455179","https://openalex.org/W2941087316","https://openalex.org/W2963054110","https://openalex.org/W2963710203","https://openalex.org/W2972408125","https://openalex.org/W2999080214","https://openalex.org/W3134938427","https://openalex.org/W3192045553","https://openalex.org/W3202002893","https://openalex.org/W3202146850","https://openalex.org/W4200465713","https://openalex.org/W4206179284","https://openalex.org/W4221049575","https://openalex.org/W4229451493","https://openalex.org/W4248932870"],"related_works":["https://openalex.org/W4361297048","https://openalex.org/W4404118787","https://openalex.org/W4386977444","https://openalex.org/W4377864431","https://openalex.org/W4200465713","https://openalex.org/W3202002893","https://openalex.org/W4226350018","https://openalex.org/W4394923945","https://openalex.org/W4383604772","https://openalex.org/W4404192923"],"abstract_inverted_index":{"The":[0,13,64],"logarithmic":[1,17,28,62,82],"coefficients":[2,18,29,37,83],"are":[3,61],"very":[4],"essential":[5],"in":[6],"the":[7,16,22,25,35,47,56,73,77],"problems":[8],"of":[9,15,30,38,67,81,84],"univalent":[10,39],"functions":[11,40,87],"theory.":[12],"importance":[14],"is":[19,52,70],"due":[20],"to":[21,34,43,54,71],"fact":[23],"that":[24],"bounds":[26,75],"on":[27],"f":[31],"can":[32],"transfer":[33],"Taylor":[36],"themselves":[41],"or":[42],"their":[44],"powers,":[45],"via":[46],"Lebedev\u2013Milin":[48],"inequalities;":[49],"therefore,":[50],"it":[51],"interesting":[53],"investigate":[55],"Hankel":[57,79],"determinant":[58,80],"whose":[59],"entries":[60],"coefficients.":[63],"main":[65],"purpose":[66],"this":[68],"paper":[69],"obtain":[72],"sharp":[74],"for":[76],"second":[78],"strongly":[85,89],"starlike":[86],"and":[88],"convex":[90],"functions.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-07-29T00:00:00"}