{"id":"https://openalex.org/W4310207318","doi":"https://doi.org/10.3390/axioms11120680","title":"An Application of Rabotnov Functions on Certain Subclasses of Bi-Univalent Functions","display_name":"An Application of Rabotnov Functions on Certain Subclasses of Bi-Univalent Functions","publication_year":2022,"publication_date":"2022-11-28","ids":{"openalex":"https://openalex.org/W4310207318","doi":"https://doi.org/10.3390/axioms11120680"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11120680","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11120680","pdf_url":"https://www.mdpi.com/2075-1680/11/12/680/pdf?version=1671522047","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,"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"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/12/680/pdf?version=1671522047","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091401373","display_name":"Ala Amourah","orcid":"https://orcid.org/0000-0001-9287-7704"},"institutions":[{"id":"https://openalex.org/I97864281","display_name":"Irbid National University","ror":"https://ror.org/00xfxvy87","country_code":"JO","type":"education","lineage":["https://openalex.org/I97864281"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Ala Amourah","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-9287-7704","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan","institution_ids":["https://openalex.org/I97864281"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067787464","display_name":"Ibtisam Aldawish","orcid":"https://orcid.org/0000-0003-0745-3347"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Ibtisam Aldawish","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh 11564, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-0745-3347","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh 11564, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035271747","display_name":"Khadeejah Rasheed Alhindi","orcid":"https://orcid.org/0000-0003-1996-2579"},"institutions":[{"id":"https://openalex.org/I76571253","display_name":"Imam Abdulrahman Bin Faisal University","ror":"https://ror.org/038cy8j79","country_code":"SA","type":"education","lineage":["https://openalex.org/I76571253"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khadeejah Rasheed Alhindi","raw_affiliation_strings":["Department of Computer Science, College of Computer Science and Information Technology, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1996-2579","affiliations":[{"raw_affiliation_string":"Department of Computer Science, College of Computer Science and Information Technology, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441, Saudi Arabia","institution_ids":["https://openalex.org/I76571253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040041703","display_name":"Basem Aref Frasin","orcid":"https://orcid.org/0000-0001-8608-8063"},"institutions":[{"id":"https://openalex.org/I31079310","display_name":"Al al-Bayt University","ror":"https://ror.org/028jh2126","country_code":"JO","type":"education","lineage":["https://openalex.org/I31079310"]}],"countries":["JO"],"is_corresponding":true,"raw_author_name":"Basem Aref Frasin","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-8608-8063","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan","institution_ids":["https://openalex.org/I31079310"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040041703","https://openalex.org/A5067787464"],"corresponding_institution_ids":["https://openalex.org/I240666556","https://openalex.org/I31079310"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":2.6567,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.90830022,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":"12","first_page":"680","last_page":"680"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9725000262260437,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9273999929428101,"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/variety","display_name":"Variety (cybernetics)","score":0.6785173416137695},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5788025259971619},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5691914558410645},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5069344639778137},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3208957314491272},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15718761086463928},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07288634777069092},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04036444425582886}],"concepts":[{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6785173416137695},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5788025259971619},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5691914558410645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5069344639778137},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3208957314491272},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15718761086463928},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07288634777069092},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04036444425582886}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11120680","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11120680","pdf_url":"https://www.mdpi.com/2075-1680/11/12/680/pdf?version=1671522047","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,"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:23173471cbdd41e6ae7faa7c534ceba0","is_oa":true,"landing_page_url":"https://doaj.org/article/23173471cbdd41e6ae7faa7c534ceba0","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":"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 12, p 680 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/12/680/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11120680","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":"Axioms; Volume 11; Issue 12; Pages: 680","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11120680","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11120680","pdf_url":"https://www.mdpi.com/2075-1680/11/12/680/pdf?version=1671522047","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,"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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4310207318.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W7495140","https://openalex.org/W1963790780","https://openalex.org/W2011832794","https://openalex.org/W2039692239","https://openalex.org/W2046051422","https://openalex.org/W2054180108","https://openalex.org/W2073251095","https://openalex.org/W2134197866","https://openalex.org/W2277670494","https://openalex.org/W2327672688","https://openalex.org/W2484044808","https://openalex.org/W2894519081","https://openalex.org/W2899498789","https://openalex.org/W2954358791","https://openalex.org/W3093697257","https://openalex.org/W3201689145","https://openalex.org/W4206378540","https://openalex.org/W4223925996","https://openalex.org/W4224993594","https://openalex.org/W4281865573","https://openalex.org/W4282826335","https://openalex.org/W4285733470","https://openalex.org/W4298134413","https://openalex.org/W6600291704","https://openalex.org/W6653366778","https://openalex.org/W6766538240"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"a":[3,45],"new":[4,48],"class":[5],"R\u03a3\u03bc(x,\u03b3,\u03b1,\u03b4,\u03b2)":[6,38],"of":[7,13,24,47],"bi-univalent":[8],"functions":[9,19,35],"studied":[10],"by":[11,52],"means":[12],"Gegenbauer":[14],"polynomials":[15],"(GP)":[16],"with":[17],"Rabotnov":[18],"is":[20],"introduced.":[21],"The":[22],"coefficient":[23],"the":[25,54,57],"Taylor":[26],"coefficients":[27],"a2":[28],"and":[29,31],"a3":[30],"Fekete-Szeg\u00f6":[32],"problems":[33],"for":[34],"belonging":[36],"to":[37],"have":[39],"been":[40],"derived":[41],"as":[42],"well.":[43],"Furthermore,":[44],"variety":[46],"results":[49],"will":[50],"appear":[51],"considering":[53],"parameters":[55],"in":[56],"main":[58],"results.":[59]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2022-11-30T00:00:00"}