{"id":"https://openalex.org/W4391752652","doi":"https://doi.org/10.3390/sym16020218","title":"Applications of Horadam Polynomials for Bazilevi\u010d and \u03bb-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions","display_name":"Applications of Horadam Polynomials for Bazilevi\u010d and \u03bb-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions","publication_year":2024,"publication_date":"2024-02-11","ids":{"openalex":"https://openalex.org/W4391752652","doi":"https://doi.org/10.3390/sym16020218"},"language":"en","primary_location":{"id":"doi:10.3390/sym16020218","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020218","pdf_url":"https://www.mdpi.com/2073-8994/16/2/218/pdf?version=1707628686","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","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/2/218/pdf?version=1707628686","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000466489","display_name":"Isra Al-Shbeil","orcid":"https://orcid.org/0000-0001-5287-4656"},"institutions":[{"id":"https://openalex.org/I114972647","display_name":"University of Jordan","ror":"https://ror.org/05k89ew48","country_code":"JO","type":"education","lineage":["https://openalex.org/I114972647"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Isra Al-Shbeil","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-5287-4656","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan","institution_ids":["https://openalex.org/I114972647"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071027563","display_name":"Abbas Kareem Wanas","orcid":"https://orcid.org/0000-0001-5838-7365"},"institutions":[{"id":"https://openalex.org/I4210126504","display_name":"University of Al-Qadisiyah","ror":"https://ror.org/02ewzwr87","country_code":"IQ","type":"education","lineage":["https://openalex.org/I4210126504"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Abbas Kareem Wanas","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58001, Iraq"],"raw_orcid":"https://orcid.org/0000-0001-5838-7365","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58001, Iraq","institution_ids":["https://openalex.org/I4210126504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026603696","display_name":"Hala Alaqad","orcid":null},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Hala AlAqad","raw_affiliation_strings":["Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013745777","display_name":"Adriana C\u0103ta\u015f","orcid":"https://orcid.org/0000-0002-1000-7375"},"institutions":[{"id":"https://openalex.org/I162871001","display_name":"University of Oradea","ror":"https://ror.org/00wzhv093","country_code":"RO","type":"education","lineage":["https://openalex.org/I162871001"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Adriana C\u0103ta\u015f","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania"],"raw_orcid":"https://orcid.org/0000-0002-1000-7375","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania","institution_ids":["https://openalex.org/I162871001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092690151","display_name":"Hanan Alohali","orcid":"https://orcid.org/0009-0005-0052-4976"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hanan Alohali","raw_affiliation_strings":["Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0005-0052-4976","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5013745777"],"corresponding_institution_ids":["https://openalex.org/I162871001"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.8477,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.96503094,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"16","issue":"2","first_page":"218","last_page":"218"},"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/T13335","display_name":"Pharmacological Effects of Medicinal Plants","score":0.9083999991416931,"subfield":{"id":"https://openalex.org/subfields/2736","display_name":"Pharmacology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6253455877304077},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6046565771102905},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5790682435035706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5605738162994385},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.4637812376022339},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.45804399251937866},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.415246844291687},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39214062690734863},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23606979846954346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17021360993385315},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05874881148338318}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6253455877304077},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6046565771102905},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5790682435035706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5605738162994385},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.4637812376022339},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.45804399251937866},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.415246844291687},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39214062690734863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23606979846954346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17021360993385315},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05874881148338318},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16020218","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020218","pdf_url":"https://www.mdpi.com/2073-8994/16/2/218/pdf?version=1707628686","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:doaj.org/article:11342d628f5144619f0ee4e33bf5b1d4","is_oa":false,"landing_page_url":"https://doaj.org/article/11342d628f5144619f0ee4e33bf5b1d4","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,"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":"Symmetry, Vol 16, Iss 2, p 218 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16020218","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020218","pdf_url":"https://www.mdpi.com/2073-8994/16/2/218/pdf?version=1707628686","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/G2716117995","display_name":null,"funder_award_id":"RSPD2024R860","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391752652.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W7495140","https://openalex.org/W88721985","https://openalex.org/W2039692239","https://openalex.org/W2134197866","https://openalex.org/W2401870400","https://openalex.org/W2473130221","https://openalex.org/W2562512100","https://openalex.org/W2567530644","https://openalex.org/W2737657891","https://openalex.org/W2761672173","https://openalex.org/W2798021082","https://openalex.org/W2899498789","https://openalex.org/W2900018998","https://openalex.org/W2904353761","https://openalex.org/W2963397829","https://openalex.org/W2976804790","https://openalex.org/W2981534252","https://openalex.org/W2991077540","https://openalex.org/W3004277151","https://openalex.org/W3183325902","https://openalex.org/W3214633825","https://openalex.org/W4213388323","https://openalex.org/W4233886660","https://openalex.org/W4293104762","https://openalex.org/W4296239733","https://openalex.org/W4313588313","https://openalex.org/W4319298570","https://openalex.org/W4360615889","https://openalex.org/W4366547661","https://openalex.org/W4367181730","https://openalex.org/W4380632830","https://openalex.org/W4387140973","https://openalex.org/W4388233847","https://openalex.org/W4402831577","https://openalex.org/W6600291704","https://openalex.org/W6643271403"],"related_works":["https://openalex.org/W2395105737","https://openalex.org/W2369507325","https://openalex.org/W3208270790","https://openalex.org/W2994244880","https://openalex.org/W3135719690","https://openalex.org/W2368550193","https://openalex.org/W1985023705","https://openalex.org/W2061027733","https://openalex.org/W2387252559","https://openalex.org/W2032389377"],"abstract_inverted_index":{"In":[0],"this":[1,74],"study,":[2],"we":[3,63],"introduce":[4],"a":[5],"new":[6],"class":[7],"of":[8],"normalized":[9],"analytic":[10],"and":[11,25,34,50,60,69],"bi-univalent":[12],"functions":[13,18,24,47],"denoted":[14],"by":[15],"D\u03a3(\u03b4,\u03b7,\u03bb,t,r).":[16],"These":[17],"are":[19],"connected":[20],"to":[21],"the":[22,26,42,46,55],"Bazilevi\u010d":[23],"\u03bb-pseudo-starlike":[27],"functions.":[28],"We":[29,40],"employ":[30],"Sakaguchi":[31],"Type":[32],"Functions":[33],"Horadam":[35],"polynomials":[36],"in":[37,48],"our":[38,67],"survey.":[39],"establish":[41,64],"Fekete-Szeg\u00f6":[43],"inequality":[44],"for":[45,54],"D\u03a3(\u03b4,\u03b7,\u03bb,t,r)":[49],"derive":[51],"upper":[52],"bounds":[53],"initial":[56],"Taylor\u2013Maclaurin":[57],"coefficients":[58],"|a2|":[59],"|a3|.":[61],"Additionally,":[62],"connections":[65],"between":[66],"results":[68],"previous":[70],"research":[71],"papers":[72],"on":[73],"topic.":[75]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2024-02-13T00:00:00"}