{"id":"https://openalex.org/W4407749671","doi":"https://doi.org/10.3390/sym17020310","title":"Coefficient Estimates in a Class of Close-to-Convex Functions","display_name":"Coefficient Estimates in a Class of Close-to-Convex Functions","publication_year":2025,"publication_date":"2025-02-19","ids":{"openalex":"https://openalex.org/W4407749671","doi":"https://doi.org/10.3390/sym17020310"},"language":"en","primary_location":{"id":"doi:10.3390/sym17020310","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020310","pdf_url":"https://www.mdpi.com/2073-8994/17/2/310/pdf?version=1739960815","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/2073-8994/17/2/310/pdf?version=1739960815","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086836204","display_name":"Lucyna Trojnar-Spelina","orcid":"https://orcid.org/0000-0002-9210-3757"},"institutions":[{"id":"https://openalex.org/I111664937","display_name":"Rzesz\u00f3w University of Technology","ror":"https://ror.org/056xse072","country_code":"PL","type":"education","lineage":["https://openalex.org/I111664937"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Lucyna Trojnar-Spelina","raw_affiliation_strings":["The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I111664937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086836204"],"corresponding_institution_ids":["https://openalex.org/I111664937"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06516531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"2","first_page":"310","last_page":"310"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9973000288009644,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9965000152587891,"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/class","display_name":"Class (philosophy)","score":0.6002494692802429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5733926296234131},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49799108505249023},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.41279780864715576},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3385096490383148},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3313817083835602},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3205275535583496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2098465859889984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.140022873878479},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11889386177062988}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6002494692802429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5733926296234131},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49799108505249023},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.41279780864715576},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3385096490383148},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3313817083835602},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3205275535583496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2098465859889984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.140022873878479},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11889386177062988}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17020310","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020310","pdf_url":"https://www.mdpi.com/2073-8994/17/2/310/pdf?version=1739960815","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"}],"best_oa_location":{"id":"doi:10.3390/sym17020310","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020310","pdf_url":"https://www.mdpi.com/2073-8994/17/2/310/pdf?version=1739960815","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407749671.pdf","grobid_xml":"https://content.openalex.org/works/W4407749671.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W302011477","https://openalex.org/W1985494759","https://openalex.org/W2011687176","https://openalex.org/W2016076454","https://openalex.org/W2022376763","https://openalex.org/W2033170782","https://openalex.org/W2050144314","https://openalex.org/W2116559667","https://openalex.org/W2134197866","https://openalex.org/W2783438107","https://openalex.org/W2947142224","https://openalex.org/W2962733239","https://openalex.org/W3001463643","https://openalex.org/W3035734900","https://openalex.org/W3093931628","https://openalex.org/W4388534025","https://openalex.org/W4405471501","https://openalex.org/W6641636988","https://openalex.org/W6705303006","https://openalex.org/W6747073834"],"related_works":["https://openalex.org/W2368454205","https://openalex.org/W2370467235","https://openalex.org/W2989824750","https://openalex.org/W2347925354","https://openalex.org/W4238050384","https://openalex.org/W2359737466","https://openalex.org/W2800924481","https://openalex.org/W2110671666","https://openalex.org/W2366306114","https://openalex.org/W4387635768"],"abstract_inverted_index":{"In":[0,30,51,66],"this":[1,31,49,81],"paper,":[2,32],"we":[3,33,53,68],"consider":[4,54],"analytic":[5],"functions":[6,20,47],"with":[7],"the":[8,25,42,60,77],"formalization":[9],"f(0)=f\u2032(0)\u22121=0,":[10],"which":[11],"satisfy":[12],"Re{(1\u2212\u03b1z2)f\u2032(z)}>0,z\u2208\u0394={z\u2208C:|z|<1},":[13],"where":[14,39],"\u03b1\u2208[\u22121,1].":[15],"The":[16],"set":[17],"of":[18,24,27,37,71,74],"such":[19],"is":[21,41,64],"a":[22],"subclass":[23],"class":[26,79],"close-to-convex":[28],"functions.":[29],"present":[34],"sharp":[35],"bounds":[36,70],"|an|,":[38],"an":[40],"n\u2212th":[43],"Taylor\u2019s":[44],"coefficients":[45],"for":[46,76],"in":[48],"class.":[50],"addition,":[52],"several":[55],"symmetric":[56],"coefficient":[57,62],"problems":[58],"when":[59],"second":[61],"a2":[63],"established.":[65],"particular,":[67],"provide":[69],"|an+1\u2212an|":[72],"and":[73],"|2na2n\u2212(2n\u22121)a2n\u22121|":[75],"considered":[78],"under":[80],"additional":[82],"assumption.":[83]},"counts_by_year":[],"updated_date":"2026-03-08T06:56:09.383167","created_date":"2025-10-10T00:00:00"}