{"id":"https://openalex.org/W3169049758","doi":"https://doi.org/10.3390/sym13060966","title":"On Certain Differential Subordination of Harmonic Mean Related to a Linear Function","display_name":"On Certain Differential Subordination of Harmonic Mean Related to a Linear Function","publication_year":2021,"publication_date":"2021-05-29","ids":{"openalex":"https://openalex.org/W3169049758","doi":"https://doi.org/10.3390/sym13060966","mag":"3169049758"},"language":"en","primary_location":{"id":"doi:10.3390/sym13060966","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060966","pdf_url":"https://www.mdpi.com/2073-8994/13/6/966/pdf?version=1622605931","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/2073-8994/13/6/966/pdf?version=1622605931","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029451837","display_name":"Anna Dobosz","orcid":"https://orcid.org/0000-0003-2289-1986"},"institutions":[{"id":"https://openalex.org/I47996466","display_name":"University of Warmia and Mazury in Olsztyn","ror":"https://ror.org/05s4feg49","country_code":"PL","type":"education","lineage":["https://openalex.org/I47996466"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Anna Dobosz","raw_affiliation_strings":["Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. S\u0142oneczna 54, 10-710 Olsztyn, Poland"],"raw_orcid":"https://orcid.org/0000-0003-2289-1986","affiliations":[{"raw_affiliation_string":"Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. S\u0142oneczna 54, 10-710 Olsztyn, Poland","institution_ids":["https://openalex.org/I47996466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014166307","display_name":"Piotr Jastrz\u0229bski","orcid":"https://orcid.org/0000-0002-1974-8305"},"institutions":[{"id":"https://openalex.org/I47996466","display_name":"University of Warmia and Mazury in Olsztyn","ror":"https://ror.org/05s4feg49","country_code":"PL","type":"education","lineage":["https://openalex.org/I47996466"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Jastrz\u0119bski","raw_affiliation_strings":["Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. S\u0142oneczna 54, 10-710 Olsztyn, Poland"],"raw_orcid":"https://orcid.org/0000-0002-1974-8305","affiliations":[{"raw_affiliation_string":"Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. S\u0142oneczna 54, 10-710 Olsztyn, Poland","institution_ids":["https://openalex.org/I47996466"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052735462","display_name":"Adam Lecko","orcid":"https://orcid.org/0000-0002-0185-9402"},"institutions":[{"id":"https://openalex.org/I47996466","display_name":"University of Warmia and Mazury in Olsztyn","ror":"https://ror.org/05s4feg49","country_code":"PL","type":"education","lineage":["https://openalex.org/I47996466"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Adam Lecko","raw_affiliation_strings":["Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. S\u0142oneczna 54, 10-710 Olsztyn, Poland"],"raw_orcid":"https://orcid.org/0000-0002-0185-9402","affiliations":[{"raw_affiliation_string":"Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. S\u0142oneczna 54, 10-710 Olsztyn, Poland","institution_ids":["https://openalex.org/I47996466"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052735462"],"corresponding_institution_ids":["https://openalex.org/I47996466"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.8054,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69912922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"13","issue":"6","first_page":"966","last_page":"966"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subordination","display_name":"Subordination (linguistics)","score":0.9188014268875122},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.7684880495071411},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.643150269985199},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5424999594688416},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.5326235890388489},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5240576267242432},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48830413818359375},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4692290723323822},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33739346265792847},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13208946585655212},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07353091239929199}],"concepts":[{"id":"https://openalex.org/C2777406531","wikidata":"https://www.wikidata.org/wiki/Q2031017","display_name":"Subordination (linguistics)","level":2,"score":0.9188014268875122},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.7684880495071411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.643150269985199},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5424999594688416},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.5326235890388489},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5240576267242432},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48830413818359375},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4692290723323822},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33739346265792847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13208946585655212},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07353091239929199},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13060966","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060966","pdf_url":"https://www.mdpi.com/2073-8994/13/6/966/pdf?version=1622605931","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:e1bc473b38794cf387353d2d20602483","is_oa":true,"landing_page_url":"https://doaj.org/article/e1bc473b38794cf387353d2d20602483","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":"Symmetry, Vol 13, Iss 6, p 966 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/6/966/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13060966","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13060966","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060966","pdf_url":"https://www.mdpi.com/2073-8994/13/6/966/pdf?version=1622605931","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3169049758.pdf","grobid_xml":"https://content.openalex.org/works/W3169049758.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1964849997","https://openalex.org/W1983511647","https://openalex.org/W2003606952","https://openalex.org/W2010132456","https://openalex.org/W2018418340","https://openalex.org/W2019413649","https://openalex.org/W2026295331","https://openalex.org/W2045033631","https://openalex.org/W2055266536","https://openalex.org/W2055493512","https://openalex.org/W2064685239","https://openalex.org/W2093737279","https://openalex.org/W2895960269","https://openalex.org/W4233886660","https://openalex.org/W6641609488","https://openalex.org/W6661707444"],"related_works":["https://openalex.org/W4362679660","https://openalex.org/W2754149008","https://openalex.org/W2734878744","https://openalex.org/W172694950","https://openalex.org/W2778103536","https://openalex.org/W1994650426","https://openalex.org/W3201797622","https://openalex.org/W2388562435","https://openalex.org/W3135211543","https://openalex.org/W4321109048"],"abstract_inverted_index":{"In":[0,28,62],"this":[1,63,89],"paper":[2,85],"we":[3],"study":[4,53],"a":[5,22,25,65,96,108],"certain":[6],"differential":[7,37,55,101,113],"subordination":[8,102],"related":[9],"to":[10,30,71,82,88],"the":[11,19,31,36,40,45,58,74,93,100,104,111],"harmonic":[12,41,105],"mean":[13,42,106],"and":[14,67,99],"its":[15],"symmetry":[16],"properties,":[17],"in":[18,43,91],"case":[20],"where":[21],"dominant":[23,46,76,94],"is":[24,70,80,86,95,107],"linear":[26,97],"function.":[27,61],"addition":[29],"known":[32],"general":[33],"results":[34],"for":[35,57,73],"subordinations":[38,56],"of":[39,103,110],"which":[44,92],"was":[47],"any":[48],"convex":[49,60],"function,":[50,98],"one":[51,78],"can":[52],"such":[54],"selected":[59],"case,":[64],"reasonable":[66],"difficult":[68],"issue":[69],"look":[72],"best":[75],"or":[77],"that":[79],"close":[81],"it.":[83],"This":[84],"devoted":[87],"issue,":[90],"generalization":[109],"Briot\u2013Bouquet":[112],"subordination.":[114]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
