{"id":"https://openalex.org/W2994718792","doi":"https://doi.org/10.3390/sym11121497","title":"On the Fekete\u2013Szeg\u00f6 Type Functionals for Close-to-Convex Functions","display_name":"On the Fekete\u2013Szeg\u00f6 Type Functionals for Close-to-Convex Functions","publication_year":2019,"publication_date":"2019-12-10","ids":{"openalex":"https://openalex.org/W2994718792","doi":"https://doi.org/10.3390/sym11121497","mag":"2994718792"},"language":"en","primary_location":{"id":"doi:10.3390/sym11121497","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121497","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1497/pdf?version=1576477311","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/12/1497/pdf?version=1576477311","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025288529","display_name":"Katarzyna Tr\u0105bka-Wi\u0119c\u0142aw","orcid":"https://orcid.org/0000-0002-1693-5367"},"institutions":[{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Katarzyna Tra\u0327bka-Wi\u0229c\u0142aw","raw_affiliation_strings":["Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland"],"raw_orcid":"https://orcid.org/0000-0002-1693-5367","affiliations":[{"raw_affiliation_string":"Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083828107","display_name":"Pawe\u0142 Zaprawa","orcid":"https://orcid.org/0000-0002-7279-9582"},"institutions":[{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Zaprawa","raw_affiliation_strings":["Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland"],"raw_orcid":"https://orcid.org/0000-0002-7279-9582","affiliations":[{"raw_affiliation_string":"Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008462830","display_name":"Magdalena Gregorczyk","orcid":"https://orcid.org/0000-0003-4612-1740"},"institutions":[{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Magdalena Gregorczyk","raw_affiliation_strings":["Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland"],"raw_orcid":"https://orcid.org/0000-0003-4612-1740","affiliations":[{"raw_affiliation_string":"Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029627936","display_name":"Andrzej Rysak","orcid":"https://orcid.org/0000-0001-9631-9785"},"institutions":[{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Andrzej Rysak","raw_affiliation_strings":["Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland"],"raw_orcid":"https://orcid.org/0000-0001-9631-9785","affiliations":[{"raw_affiliation_string":"Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5025288529"],"corresponding_institution_ids":["https://openalex.org/I8264552"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9001,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.86080357,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"12","first_page":"1497","last_page":"1497"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T14303","display_name":"Polymer Synthesis and Characterization","score":0.9560999870300293,"subfield":{"id":"https://openalex.org/subfields/2507","display_name":"Polymers and Plastics"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6639105081558228},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.6573027968406677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.649483323097229},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6312254071235657},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5967147350311279},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5599365830421448},{"id":"https://openalex.org/keywords/univalent-function","display_name":"Univalent function","score":0.5375390648841858},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4898828864097595},{"id":"https://openalex.org/keywords/logarithmically-convex-function","display_name":"Logarithmically convex function","score":0.445597380399704},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4196363389492035},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.41084423661231995},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3605194091796875},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.23228126764297485},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08590403199195862}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6639105081558228},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.6573027968406677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.649483323097229},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6312254071235657},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5967147350311279},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5599365830421448},{"id":"https://openalex.org/C178260045","wikidata":"https://www.wikidata.org/wiki/Q2608535","display_name":"Univalent function","level":3,"score":0.5375390648841858},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4898828864097595},{"id":"https://openalex.org/C136719777","wikidata":"https://www.wikidata.org/wiki/Q3610230","display_name":"Logarithmically convex function","level":5,"score":0.445597380399704},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4196363389492035},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.41084423661231995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3605194091796875},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.23228126764297485},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08590403199195862},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/sym11121497","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121497","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1497/pdf?version=1576477311","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/12/1497/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11121497","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym11121497","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121497","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1497/pdf?version=1576477311","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4946599674","display_name":null,"funder_award_id":"030/RID/2018/19","funder_id":"https://openalex.org/F4320322733","funder_display_name":"Ministerstwo Edukacji i Nauki"}],"funders":[{"id":"https://openalex.org/F4320322733","display_name":"Ministerstwo Edukacji i Nauki","ror":"https://ror.org/05dwvd537"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2994718792.pdf","grobid_xml":"https://content.openalex.org/works/W2994718792.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1024883973","https://openalex.org/W1998690851","https://openalex.org/W2003151444","https://openalex.org/W2058036837","https://openalex.org/W2076437247","https://openalex.org/W2081564218","https://openalex.org/W2083933580","https://openalex.org/W2099737046","https://openalex.org/W2110626748","https://openalex.org/W2153535232","https://openalex.org/W2256220809","https://openalex.org/W2265945549","https://openalex.org/W2523843811","https://openalex.org/W2547460859","https://openalex.org/W2588371155","https://openalex.org/W2741294992","https://openalex.org/W2765088341","https://openalex.org/W2790492860","https://openalex.org/W2810515886","https://openalex.org/W2894132440","https://openalex.org/W3098038169","https://openalex.org/W3121138390","https://openalex.org/W4248932870","https://openalex.org/W6752517455"],"related_works":["https://openalex.org/W4221012998","https://openalex.org/W3153251777","https://openalex.org/W2361933918","https://openalex.org/W4327786261","https://openalex.org/W2241099366","https://openalex.org/W2350569926","https://openalex.org/W3025126867","https://openalex.org/W2962381892","https://openalex.org/W2148416619","https://openalex.org/W2356958610"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"consider":[4],"two":[5],"functionals":[6,229],"of":[7,78,95,192,223,234],"the":[8,96,205,221],"Fekete\u2013Szeg\u00f6":[9],"type":[10,77],"\u0398":[11,141,193],"f":[12,27,51,99,109,142,148,157,194,200],"(":[13,28,52,100,111,143,149,159,164,168,195,201],"\u03bc":[14,20,29,37,45,144,150,196,202],")":[15,30,54,102,113,123,145,151,161,166,172,197,203],"=":[16,31,55,162],"a":[17,21,23,32,34,38,42,58,63,182],"4":[18,35],"\u2212":[19,36,170],"2":[22,33,40,59,61,173],"3":[24,39,64,66],"and":[25,46,84,134,146],"\u03a6":[26,147,199],"for":[41,47,91,130,135,152,208,231],"real":[43,184],"number":[44],"an":[48,178],"analytic":[49,179,235],"function":[50,180],"z":[53,56,60,65,71,101,104,112,160,165,171],"+":[57,62,67],"\u2026":[68],",":[69,116,121,174,198],"|":[70,72],"<":[73],"1":[74,122,169],".":[75,124],"This":[76],"research":[79],"was":[80],"initiated":[81],"by":[82],"Hayami":[83],"Owa":[85],"in":[86],"2010.":[87],"They":[88],"obtained":[89],"results":[90,219,225],"functions":[92,133,154,210],"satisfying":[93],"one":[94],"conditions":[97],"Re":[98,108],"/":[103,167],">":[105,114],"\u03b1":[106,115,117],"or":[107,204,211],"\u2032":[110,158],"\u2208":[118],"[":[119],"0":[120],"Similar":[125],"estimates":[126],"were":[127],"also":[128],"derived":[129],"univalent":[131,136,212,236],"starlike":[132],"convex":[137],"functions.":[138,237],"We":[139],"discuss":[140],"close-to-convex":[153,209],"such":[155],"that":[156],"h":[163,176],"where":[175],"is":[177],"with":[181,227],"positive":[183],"part.":[185],"Many":[186],"coefficient":[187],"problems,":[188],"among":[189],"others":[190],"estimating":[191],"Hankel":[206],"determinants":[207],"functions,":[213],"are":[214],"not":[215],"solved":[216],"yet.":[217],"Our":[218],"broaden":[220],"scope":[222],"theoretical":[224],"connected":[226],"these":[228],"defined":[230],"different":[232],"subclasses":[233]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}