{"id":"https://openalex.org/W4380988587","doi":"https://doi.org/10.3390/axioms12060600","title":"New Applications of Faber Polynomials and q-Fractional Calculus for a New Subclass of m-Fold Symmetric bi-Close-to-Convex Functions","display_name":"New Applications of Faber Polynomials and q-Fractional Calculus for a New Subclass of m-Fold Symmetric bi-Close-to-Convex Functions","publication_year":2023,"publication_date":"2023-06-16","ids":{"openalex":"https://openalex.org/W4380988587","doi":"https://doi.org/10.3390/axioms12060600"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12060600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12060600","pdf_url":"https://www.mdpi.com/2075-1680/12/6/600/pdf?version=1686920533","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/2075-1680/12/6/600/pdf?version=1686920533","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066920839","display_name":"Mohammad Faisal Khan","orcid":"https://orcid.org/0000-0001-5053-5028"},"institutions":[{"id":"https://openalex.org/I120238654","display_name":"Saudi Electronic University","ror":"https://ror.org/05ndh7v49","country_code":"SA","type":"education","lineage":["https://openalex.org/I120238654"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohammad Faisal Khan","raw_affiliation_strings":["Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5053-5028","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia","institution_ids":["https://openalex.org/I120238654"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029316882","display_name":"Suha B. Al-Shaikh","orcid":"https://orcid.org/0000-0002-9960-2591"},"institutions":[{"id":"https://openalex.org/I4210139873","display_name":"Arab Open University","ror":"https://ror.org/03vfnky71","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210093932","https://openalex.org/I4210139873"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Suha B. Al-Shaikh","raw_affiliation_strings":["Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-9960-2591","affiliations":[{"raw_affiliation_string":"Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia","institution_ids":["https://openalex.org/I4210139873"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044459223","display_name":"Ahmad A. Abubaker","orcid":"https://orcid.org/0000-0003-0694-1680"},"institutions":[{"id":"https://openalex.org/I4210139873","display_name":"Arab Open University","ror":"https://ror.org/03vfnky71","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210093932","https://openalex.org/I4210139873"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmad A. Abubaker","raw_affiliation_strings":["Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-0694-1680","affiliations":[{"raw_affiliation_string":"Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia","institution_ids":["https://openalex.org/I4210139873"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068483750","display_name":"Khaled Matarneh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139873","display_name":"Arab Open University","ror":"https://ror.org/03vfnky71","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210093932","https://openalex.org/I4210139873"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khaled Matarneh","raw_affiliation_strings":["Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia","institution_ids":["https://openalex.org/I4210139873"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029316882"],"corresponding_institution_ids":["https://openalex.org/I4210139873"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0631,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73248037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"12","issue":"6","first_page":"600","last_page":"600"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9765999913215637,"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/T13335","display_name":"Pharmacological Effects of Medicinal Plants","score":0.9606000185012817,"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/mathematics","display_name":"Mathematics","score":0.7282752394676208},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5559106469154358},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5512135028839111},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.54807049036026},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5312604308128357},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5300036668777466},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.510021984577179},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47040921449661255},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4656938314437866},{"id":"https://openalex.org/keywords/subclass","display_name":"Subclass","score":0.44807058572769165},{"id":"https://openalex.org/keywords/symmetric-polynomial","display_name":"Symmetric polynomial","score":0.4458160400390625},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4314473271369934},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22383832931518555},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.11197611689567566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07912978529930115},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07791003584861755}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7282752394676208},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5559106469154358},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5512135028839111},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.54807049036026},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5312604308128357},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5300036668777466},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.510021984577179},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47040921449661255},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4656938314437866},{"id":"https://openalex.org/C2776194381","wikidata":"https://www.wikidata.org/wiki/Q3965271","display_name":"Subclass","level":3,"score":0.44807058572769165},{"id":"https://openalex.org/C52153879","wikidata":"https://www.wikidata.org/wiki/Q930499","display_name":"Symmetric polynomial","level":4,"score":0.4458160400390625},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4314473271369934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22383832931518555},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.11197611689567566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07912978529930115},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07791003584861755},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C159654299","wikidata":"https://www.wikidata.org/wiki/Q79460","display_name":"Antibody","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C203014093","wikidata":"https://www.wikidata.org/wiki/Q101929","display_name":"Immunology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms12060600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12060600","pdf_url":"https://www.mdpi.com/2075-1680/12/6/600/pdf?version=1686920533","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:5553d5cab3944f539da1c053331a7bf3","is_oa":true,"landing_page_url":"https://doaj.org/article/5553d5cab3944f539da1c053331a7bf3","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 12, Iss 6, p 600 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12060600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12060600","pdf_url":"https://www.mdpi.com/2075-1680/12/6/600/pdf?version=1686920533","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/W4380988587.pdf"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W68100126","https://openalex.org/W151952532","https://openalex.org/W1763632018","https://openalex.org/W1858192235","https://openalex.org/W1910092911","https://openalex.org/W1969680751","https://openalex.org/W1975226105","https://openalex.org/W1978554979","https://openalex.org/W2001222426","https://openalex.org/W2003151444","https://openalex.org/W2008496001","https://openalex.org/W2018712748","https://openalex.org/W2027729273","https://openalex.org/W2033036473","https://openalex.org/W2039692239","https://openalex.org/W2041187841","https://openalex.org/W2049125972","https://openalex.org/W2054180108","https://openalex.org/W2074064334","https://openalex.org/W2074372080","https://openalex.org/W2074741432","https://openalex.org/W2112652736","https://openalex.org/W2114579204","https://openalex.org/W2156678972","https://openalex.org/W2288414862","https://openalex.org/W2321807852","https://openalex.org/W2326463840","https://openalex.org/W2335300816","https://openalex.org/W2515112238","https://openalex.org/W2559874564","https://openalex.org/W2567530644","https://openalex.org/W2608959249","https://openalex.org/W2922227352","https://openalex.org/W2940487400","https://openalex.org/W3001106890","https://openalex.org/W3173865866","https://openalex.org/W3196487106","https://openalex.org/W3202851793","https://openalex.org/W4200406446","https://openalex.org/W4205926841","https://openalex.org/W4206378540","https://openalex.org/W4220994213","https://openalex.org/W4221014130","https://openalex.org/W4223925996","https://openalex.org/W4224597188","https://openalex.org/W4280543061","https://openalex.org/W4281775325","https://openalex.org/W4298003818","https://openalex.org/W4309708732","https://openalex.org/W4318218471","https://openalex.org/W4318616229","https://openalex.org/W4320485633","https://openalex.org/W4322500528","https://openalex.org/W4322770528","https://openalex.org/W4360615889","https://openalex.org/W6637844332","https://openalex.org/W6650463266","https://openalex.org/W6663097149"],"related_works":["https://openalex.org/W2807382084","https://openalex.org/W4282813460","https://openalex.org/W3013709019","https://openalex.org/W1560962904","https://openalex.org/W641273746","https://openalex.org/W2093479061","https://openalex.org/W2901510162","https://openalex.org/W1597165749","https://openalex.org/W2947420081","https://openalex.org/W2178397182"],"abstract_inverted_index":{"Using":[0],"the":[1,32,43,50,58,62,66,71,76],"concepts":[2],"of":[3,26,65,70,80,101],"q-fractional":[4],"calculus":[5],"operator":[6],"theory,":[7],"we":[8,15,30,97],"first":[9],"define":[10],"a":[11,23,38,99,106],"(\u03bb,q)-differintegral":[12],"operator,":[13],"and":[14,61,91],"then":[16],"use":[17],"m-fold":[18,81],"symmetric":[19,82],"functions":[20,72],"to":[21,56,75],"discover":[22],"new":[24],"family":[25],"bi-close-to-convex":[27,83],"functions.":[28,84],"First,":[29],"estimate":[31],"general":[33],"Taylor\u2013Maclaurin":[34],"coefficient":[35,68],"bounds":[36,69],"for":[37,105],"newly":[39,77],"established":[40,78],"class":[41,79],"using":[42],"Faber":[44,51],"polynomial":[45,52],"expansion":[46],"method.":[47],"In":[48],"addition,":[49],"method":[53],"is":[54],"used":[55],"examine":[57],"Fekete\u2013Szeg\u00f6":[59],"problem":[60],"unpredictable":[63],"behavior":[64],"initial":[67],"that":[73],"belong":[74],"Our":[85],"key":[86],"results":[87],"are":[88],"both":[89],"novel":[90],"consistent":[92],"with":[93],"prior":[94],"research,":[95],"so":[96],"highlight":[98],"few":[100],"their":[102],"important":[103],"corollaries":[104],"comparison.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-06-17T00:00:00"}