{"id":"https://openalex.org/W4280646343","doi":"https://doi.org/10.3390/axioms11050236","title":"Bounds for the Neuman\u2013S\u00e1ndor Mean in Terms of the Arithmetic and Contra-Harmonic Means","display_name":"Bounds for the Neuman\u2013S\u00e1ndor Mean in Terms of the Arithmetic and Contra-Harmonic Means","publication_year":2022,"publication_date":"2022-05-19","ids":{"openalex":"https://openalex.org/W4280646343","doi":"https://doi.org/10.3390/axioms11050236"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11050236","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050236","pdf_url":"https://www.mdpi.com/2075-1680/11/5/236/pdf?version=1652950030","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/2075-1680/11/5/236/pdf?version=1652950030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050190752","display_name":"Wen Hui Li","orcid":"https://orcid.org/0000-0002-1848-8855"},"institutions":[{"id":"https://openalex.org/I4210091712","display_name":"Zhengzhou University of Science and Technology","ror":"https://ror.org/00b3j7936","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210091712"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen-Hui Li","raw_affiliation_strings":["Department of Basic Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, China"],"affiliations":[{"raw_affiliation_string":"Department of Basic Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, China","institution_ids":["https://openalex.org/I4210091712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087811002","display_name":"Peng Miao","orcid":"https://orcid.org/0000-0002-9244-3428"},"institutions":[{"id":"https://openalex.org/I4210091712","display_name":"Zhengzhou University of Science and Technology","ror":"https://ror.org/00b3j7936","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210091712"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Miao","raw_affiliation_strings":["Department of Basic Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, China"],"affiliations":[{"raw_affiliation_string":"Department of Basic Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, China","institution_ids":["https://openalex.org/I4210091712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073122046","display_name":"Bai\u2010Ni Guo","orcid":"https://orcid.org/0000-0001-6156-2590"},"institutions":[{"id":"https://openalex.org/I4210166499","display_name":"Henan Polytechnic University","ror":"https://ror.org/05vr1c885","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166499"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bai-Ni Guo","raw_affiliation_strings":["School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China","institution_ids":["https://openalex.org/I4210166499"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073122046"],"corresponding_institution_ids":["https://openalex.org/I4210166499"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.1094,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.86269785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"5","first_page":"236","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998999834060669,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998999834060669,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9908999800682068,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9642000198364258,"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/harmonic-mean","display_name":"Harmonic mean","score":0.7759529948234558},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.7447062134742737},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.6955698728561401},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.6742792129516602},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6501302123069763},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6379910111427307},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.5775781869888306},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5503928661346436},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4161801338195801},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28234052658081055},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2311374843120575},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08203202486038208},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.0751228928565979},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04501178860664368}],"concepts":[{"id":"https://openalex.org/C203858083","wikidata":"https://www.wikidata.org/wiki/Q188347","display_name":"Harmonic mean","level":2,"score":0.7759529948234558},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.7447062134742737},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.6955698728561401},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.6742792129516602},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6501302123069763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6379910111427307},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.5775781869888306},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5503928661346436},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4161801338195801},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28234052658081055},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2311374843120575},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08203202486038208},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0751228928565979},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04501178860664368},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11050236","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050236","pdf_url":"https://www.mdpi.com/2075-1680/11/5/236/pdf?version=1652950030","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:9bae0372fed548529e18e7884608705c","is_oa":true,"landing_page_url":"https://doaj.org/article/9bae0372fed548529e18e7884608705c","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":"Axioms, Vol 11, Iss 5, p 236 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/5/236/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11050236","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 5; Pages: 236","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11050236","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050236","pdf_url":"https://www.mdpi.com/2075-1680/11/5/236/pdf?version=1652950030","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":[{"score":0.550000011920929,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280646343.pdf","grobid_xml":"https://content.openalex.org/works/W4280646343.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W129559465","https://openalex.org/W1965708978","https://openalex.org/W1972282388","https://openalex.org/W2034371370","https://openalex.org/W2058988915","https://openalex.org/W2059294605","https://openalex.org/W2079025955","https://openalex.org/W2317678635","https://openalex.org/W2329882461","https://openalex.org/W2761570349","https://openalex.org/W2951198967","https://openalex.org/W3099712171","https://openalex.org/W3101208282","https://openalex.org/W3102685724","https://openalex.org/W4220816238","https://openalex.org/W4246293990","https://openalex.org/W4392893655","https://openalex.org/W6699743551"],"related_works":["https://openalex.org/W95230609","https://openalex.org/W2983300459","https://openalex.org/W1775321609","https://openalex.org/W2358475213","https://openalex.org/W2967636333","https://openalex.org/W2914880596","https://openalex.org/W4226341002","https://openalex.org/W1559834326","https://openalex.org/W2358582134","https://openalex.org/W4280646343"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,13,19],"authors":[4],"provide":[5],"several":[6],"sharp":[7,28],"upper":[8],"and":[9,21,24,34],"lower":[10],"bounds":[11],"for":[12],"Neuman\u2013S\u00e1ndor":[14],"mean":[15],"in":[16],"terms":[17],"of":[18],"arithmetic":[20],"contra-harmonic":[22],"means,":[23],"present":[25],"some":[26],"new":[27],"inequalities":[29],"involving":[30],"hyperbolic":[31,35],"sine":[32],"function":[33],"cosine":[36],"function.":[37]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}