{"id":"https://openalex.org/W4389300037","doi":"https://doi.org/10.3390/sym15122156","title":"Sharp Estimates Involving a Generalized Symmetric S\u0103l\u0103gean q-Differential Operator for Harmonic Functions via Quantum Calculus","display_name":"Sharp Estimates Involving a Generalized Symmetric S\u0103l\u0103gean q-Differential Operator for Harmonic Functions via Quantum Calculus","publication_year":2023,"publication_date":"2023-12-04","ids":{"openalex":"https://openalex.org/W4389300037","doi":"https://doi.org/10.3390/sym15122156"},"language":"en","primary_location":{"id":"doi:10.3390/sym15122156","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15122156","pdf_url":"https://www.mdpi.com/2073-8994/15/12/2156/pdf?version=1701682940","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/2073-8994/15/12/2156/pdf?version=1701682940","any_repository_has_fulltext":true},"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"],"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/A5088682741","display_name":"Shahid Khan","orcid":"https://orcid.org/0000-0003-0361-4887"},"institutions":[{"id":"https://openalex.org/I3131573596","display_name":"Abbottabad University of Science and Technology","ror":"https://ror.org/0549hdw45","country_code":"PK","type":"education","lineage":["https://openalex.org/I3131573596"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shahid Khan","raw_affiliation_strings":["Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan","Department of Mathematics, Abbottabad University of Science and Technology Abbottabad, Abbottabad 22500, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan","institution_ids":["https://openalex.org/I3131573596"]},{"raw_affiliation_string":"Department of Mathematics, Abbottabad University of Science and Technology Abbottabad, Abbottabad 22500, Pakistan","institution_ids":["https://openalex.org/I3131573596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087794334","display_name":"Fairouz Tchier","orcid":"https://orcid.org/0000-0001-7855-508X"},"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":"Fairouz Tchier","raw_affiliation_strings":["Mathematics Department, College of Science, King Saud University, Riyadh 11495, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, College of Science, King Saud University, Riyadh 11495, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014846306","display_name":"Ferdous M. O. Tawfiq","orcid":"https://orcid.org/0000-0003-1655-5185"},"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":"Ferdous M. O. Tawfiq","raw_affiliation_strings":["Mathematics Department, College of Science, King Saud University, Riyadh 11495, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, College of Science, King Saud University, Riyadh 11495, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008509757","display_name":"Amani Shatarah","orcid":null},"institutions":[{"id":"https://openalex.org/I23075662","display_name":"Taibah University","ror":"https://ror.org/01xv1nn60","country_code":"SA","type":"education","lineage":["https://openalex.org/I23075662"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Amani Shatarah","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Arts, Taibah University, Al-Madinah 42353, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Arts, Taibah University, Al-Madinah 42353, Saudi Arabia","institution_ids":["https://openalex.org/I23075662"]}]},{"author_position":"last","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"],"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"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"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":1.0972,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.77683284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"15","issue":"12","first_page":"2156","last_page":"2156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9896000027656555,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.942799985408783,"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/mathematics","display_name":"Mathematics","score":0.7303876876831055},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.7121070623397827},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6911322474479675},{"id":"https://openalex.org/keywords/differential-calculus","display_name":"Differential calculus","score":0.5488265156745911},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4951709806919098},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4625512957572937},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.4538574814796448},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.4203653335571289},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41887474060058594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41416192054748535},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.4135088324546814},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3762466013431549},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36119818687438965},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2234100103378296},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15845277905464172},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1209256649017334}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7303876876831055},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.7121070623397827},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6911322474479675},{"id":"https://openalex.org/C56802139","wikidata":"https://www.wikidata.org/wiki/Q149999","display_name":"Differential calculus","level":2,"score":0.5488265156745911},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4951709806919098},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4625512957572937},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.4538574814796448},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.4203653335571289},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41887474060058594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41416192054748535},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.4135088324546814},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3762466013431549},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36119818687438965},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2234100103378296},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15845277905464172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1209256649017334},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym15122156","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15122156","pdf_url":"https://www.mdpi.com/2073-8994/15/12/2156/pdf?version=1701682940","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:a25584219f0348d0b92e29d88eb4946c","is_oa":true,"landing_page_url":"https://doaj.org/article/a25584219f0348d0b92e29d88eb4946c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 12, p 2156 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15122156","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15122156","pdf_url":"https://www.mdpi.com/2073-8994/15/12/2156/pdf?version=1701682940","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/G1343954612","display_name":null,"funder_award_id":"RSP2023R44","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"},{"id":"https://openalex.org/G3185388506","display_name":null,"funder_award_id":"RSP2023R4","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"},{"id":"https://openalex.org/G3210792610","display_name":null,"funder_award_id":"RSP2023R440","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"},{"id":"https://openalex.org/G8239988234","display_name":null,"funder_award_id":"Riyadh","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":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389300037.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W26190571","https://openalex.org/W1541084929","https://openalex.org/W1950030264","https://openalex.org/W1965158021","https://openalex.org/W1988126813","https://openalex.org/W1988953911","https://openalex.org/W1999270732","https://openalex.org/W2009571968","https://openalex.org/W2059984780","https://openalex.org/W2064329444","https://openalex.org/W2073367694","https://openalex.org/W2074399320","https://openalex.org/W2078924081","https://openalex.org/W2085082416","https://openalex.org/W2321807852","https://openalex.org/W2331095099","https://openalex.org/W2510611020","https://openalex.org/W2804716337","https://openalex.org/W2943572681","https://openalex.org/W2962885190","https://openalex.org/W3033421294","https://openalex.org/W3100956195","https://openalex.org/W3207822063","https://openalex.org/W4220847496","https://openalex.org/W4284893891","https://openalex.org/W4297147901","https://openalex.org/W4302911103","https://openalex.org/W4360615889","https://openalex.org/W4380142946","https://openalex.org/W4384823293","https://openalex.org/W6608190259","https://openalex.org/W6632562538","https://openalex.org/W6762478612","https://openalex.org/W6765692219","https://openalex.org/W6783862982","https://openalex.org/W6842685866"],"related_works":["https://openalex.org/W2074399320","https://openalex.org/W1546801208","https://openalex.org/W2058893028","https://openalex.org/W4287878598","https://openalex.org/W3135480182","https://openalex.org/W4318474124","https://openalex.org/W3017284032","https://openalex.org/W2279921290","https://openalex.org/W1565751200","https://openalex.org/W2992685847"],"abstract_inverted_index":{"In":[0],"this":[1,85],"study,":[2],"we":[3,71,74],"apply":[4],"q-symmetric":[5],"calculus":[6],"operator":[7,16,30],"theory":[8],"and":[9,31,59,81],"investigate":[10],"a":[11,27,64],"generalized":[12],"symmetric":[13],"S\u0103l\u0103gean":[14],"q-differential":[15],"for":[17,63],"harmonic":[18,36,68],"functions":[19,37],"in":[20,38],"an":[21],"open":[22],"unit":[23],"disk.":[24],"We":[25,41],"consider":[26],"newly":[28],"defined":[29],"establish":[32],"new":[33,65],"subclasses":[34],"of":[35,55,67,78,84],"complex":[39],"order.":[40],"determine":[42],"the":[43,48,53,60,76,82],"sharp":[44],"results,":[45],"such":[46],"as":[47],"sufficient":[49],"necessary":[50],"coefficient":[51],"bounds,":[52],"extreme":[54],"closed":[56],"convex":[57],"hulls,":[58],"distortion":[61],"theorems":[62],"family":[66],"functions.":[69],"Further,":[70],"illustrate":[72],"how":[73],"connect":[75],"findings":[77],"previous":[79],"studies":[80],"results":[83],"article.":[86]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2023-12-05T00:00:00"}