{"id":"https://openalex.org/W4409313894","doi":"https://doi.org/10.3390/sym17040558","title":"Classes of Harmonic Functions Defined by the Carlson\u2013Shaffer Operator","display_name":"Classes of Harmonic Functions Defined by the Carlson\u2013Shaffer Operator","publication_year":2025,"publication_date":"2025-04-06","ids":{"openalex":"https://openalex.org/W4409313894","doi":"https://doi.org/10.3390/sym17040558"},"language":"en","primary_location":{"id":"doi:10.3390/sym17040558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040558","pdf_url":"https://www.mdpi.com/2073-8994/17/4/558/pdf?version=1743949591","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/2073-8994/17/4/558/pdf?version=1743949591","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052327270","display_name":"Jacek Dziok","orcid":"https://orcid.org/0000-0003-1482-1080"},"institutions":[{"id":"https://openalex.org/I98559091","display_name":"Rzesz\u00f3w University","ror":"https://ror.org/03pfsnq21","country_code":"PL","type":"education","lineage":["https://openalex.org/I98559091"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Jacek Dziok","raw_affiliation_strings":["Institute of Mathematics, University of Rzesz\u00f3w, 35-310 Rzesz\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Rzesz\u00f3w, 35-310 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I98559091","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052327270"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I98559091"],"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":0.12075793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"4","first_page":"558","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9975000023841858,"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":0.9962000250816345,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5531483888626099},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5233320593833923},{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.4853436052799225},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4113611876964569},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3922390937805176},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3313504457473755},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2575303316116333},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.10339853167533875},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.08302974700927734}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5531483888626099},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5233320593833923},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.4853436052799225},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4113611876964569},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3922390937805176},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3313504457473755},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2575303316116333},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.10339853167533875},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08302974700927734},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17040558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040558","pdf_url":"https://www.mdpi.com/2073-8994/17/4/558/pdf?version=1743949591","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/sym17040558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040558","pdf_url":"https://www.mdpi.com/2073-8994/17/4/558/pdf?version=1743949591","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/W4409313894.pdf","grobid_xml":"https://content.openalex.org/works/W4409313894.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1586016240","https://openalex.org/W1979839841","https://openalex.org/W1981771500","https://openalex.org/W1988126813","https://openalex.org/W2004025098","https://openalex.org/W2017520442","https://openalex.org/W2046073694","https://openalex.org/W2058893028","https://openalex.org/W2059984780","https://openalex.org/W2074399320","https://openalex.org/W2078952312","https://openalex.org/W2079295328","https://openalex.org/W2084822343","https://openalex.org/W2090842005","https://openalex.org/W2181930695","https://openalex.org/W2803451703","https://openalex.org/W2943933468","https://openalex.org/W4212930149","https://openalex.org/W4388623065","https://openalex.org/W4408296201","https://openalex.org/W6707541840"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1973641256","https://openalex.org/W2089274067","https://openalex.org/W56994397","https://openalex.org/W1121942432","https://openalex.org/W2360188928","https://openalex.org/W2887720363","https://openalex.org/W4236509407","https://openalex.org/W3193633018","https://openalex.org/W4221155962"],"abstract_inverted_index":{"The":[0,26],"Carlson\u2013Shaffer":[1,27,67],"operator":[2,28],"plays":[3],"an":[4],"important":[5],"role":[6],"in":[7,48],"the":[8,18,22,36,40,44,49,59,66,90,110],"geometric":[9],"theory":[10,50,60],"of":[11,51,61,73,92,105],"analytic":[12,52],"functions.":[13,63,93],"It":[14],"is":[15],"associated":[16],"with":[17],"hypergeometric":[19],"function":[20],"and":[21,43,85,103,107],"incomplete":[23],"beta":[24],"function.":[25],"generalizes":[29],"various":[30],"other":[31],"linear":[32],"operators,":[33],"such":[34],"as":[35],"Ruscheweyh":[37],"derivative":[38],"operator,":[39,42,68],"Bernardi\u2013Libera\u2013Livingston":[41],"Srivastava\u2013Owa":[45],"operator.":[46],"Ideas":[47],"functions":[53,75],"are":[54],"often":[55],"symmetrically":[56],"transferred":[57],"to":[58],"harmonic":[62,74],"By":[64],"using":[65],"we":[69,81,95],"introduce":[70],"a":[71],"class":[72,91],"defined":[76,111],"by":[77],"weak":[78],"subordination.":[79],"Next,":[80],"give":[82],"some":[83],"necessary":[84],"sufficient":[86],"coefficient":[87,97],"conditions":[88],"for":[89,109],"Furthermore,":[94],"determine":[96],"estimates,":[98],"distortion":[99],"bounds,":[100],"extreme":[101],"points,":[102],"radii":[104],"starlikeness":[106],"convexity":[108],"class.":[112]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}