{"id":"https://openalex.org/W4283368900","doi":"https://doi.org/10.3390/axioms11070304","title":"Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman\u2013S\u00e1ndor Mean and the First Seiffert Mean","display_name":"Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman\u2013S\u00e1ndor Mean and the First Seiffert Mean","publication_year":2022,"publication_date":"2022-06-23","ids":{"openalex":"https://openalex.org/W4283368900","doi":"https://doi.org/10.3390/axioms11070304"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11070304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11070304","pdf_url":"https://www.mdpi.com/2075-1680/11/7/304/pdf?version=1655974522","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/2075-1680/11/7/304/pdf?version=1655974522","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"],"raw_orcid":"https://orcid.org/0000-0002-1848-8855","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/A5051195090","display_name":"Qi-Xia Shen","orcid":null},"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":"Qi-Xia Shen","raw_affiliation_strings":["Department of Basic Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, China"],"raw_orcid":null,"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/I4210135633","display_name":"Dallas Independent School District","ror":"https://ror.org/03s538y47","country_code":"US","type":"education","lineage":["https://openalex.org/I4210135633"]},{"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","US"],"is_corresponding":true,"raw_author_name":"Bai-Ni Guo","raw_affiliation_strings":["Independent Researcher, Dallas, TX 75252-8024, USA","School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China"],"raw_orcid":"https://orcid.org/0000-0001-6156-2590","affiliations":[{"raw_affiliation_string":"Independent Researcher, Dallas, TX 75252-8024, USA","institution_ids":["https://openalex.org/I4210135633"]},{"raw_affiliation_string":"School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China","institution_ids":["https://openalex.org/I4210166499"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073122046"],"corresponding_institution_ids":["https://openalex.org/I4210135633","https://openalex.org/I4210166499"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.8463,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.90809048,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11","issue":"7","first_page":"304","last_page":"304"},"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":0.9873999953269958,"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/T12504","display_name":"Mathematics and Applications","score":0.9819999933242798,"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/sine","display_name":"Sine","score":0.7665947675704956},{"id":"https://openalex.org/keywords/sinc-function","display_name":"Sinc function","score":0.7579753398895264},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.7073790431022644},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.6980857253074646},{"id":"https://openalex.org/keywords/inverse-trigonometric-functions","display_name":"Inverse trigonometric functions","score":0.67157381772995},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6578484773635864},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.6399887800216675},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.637791633605957},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.5860699415206909},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4478260278701782},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.42610353231430054},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3174903392791748},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12561234831809998}],"concepts":[{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.7665947675704956},{"id":"https://openalex.org/C152303783","wikidata":"https://www.wikidata.org/wiki/Q855949","display_name":"Sinc function","level":2,"score":0.7579753398895264},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.7073790431022644},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.6980857253074646},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.67157381772995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6578484773635864},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.6399887800216675},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.637791633605957},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.5860699415206909},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4478260278701782},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42610353231430054},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3174903392791748},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12561234831809998},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11070304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11070304","pdf_url":"https://www.mdpi.com/2075-1680/11/7/304/pdf?version=1655974522","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:b24fed161a694b118db555101fb5ec53","is_oa":true,"landing_page_url":"https://doaj.org/article/b24fed161a694b118db555101fb5ec53","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 7, p 304 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/7/304/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11070304","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 7; Pages: 304","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11070304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11070304","pdf_url":"https://www.mdpi.com/2075-1680/11/7/304/pdf?version=1655974522","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":0.6399999856948853,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283368900.pdf","grobid_xml":"https://content.openalex.org/works/W4283368900.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W129559465","https://openalex.org/W208611650","https://openalex.org/W1965708978","https://openalex.org/W1982819439","https://openalex.org/W2023779735","https://openalex.org/W2034371370","https://openalex.org/W2058988915","https://openalex.org/W2123806876","https://openalex.org/W2127985757","https://openalex.org/W2139298509","https://openalex.org/W2317636930","https://openalex.org/W2324949522","https://openalex.org/W2327206911","https://openalex.org/W2329882461","https://openalex.org/W2900215169","https://openalex.org/W2964117596","https://openalex.org/W3102685724","https://openalex.org/W3167547514","https://openalex.org/W3186085134","https://openalex.org/W3208791086","https://openalex.org/W4226267126","https://openalex.org/W4230104858","https://openalex.org/W4280646343","https://openalex.org/W4304693389","https://openalex.org/W4372064109","https://openalex.org/W4391148181","https://openalex.org/W6678119358","https://openalex.org/W6765925860","https://openalex.org/W6795887699","https://openalex.org/W6860583262"],"related_works":["https://openalex.org/W2930333407","https://openalex.org/W2092000673","https://openalex.org/W3012344327","https://openalex.org/W4318472270","https://openalex.org/W2331995355","https://openalex.org/W1559834326","https://openalex.org/W610595760","https://openalex.org/W1775321609","https://openalex.org/W2888283991","https://openalex.org/W2801659468"],"abstract_inverted_index":{"In":[0],"the":[1,3,10,14,25,38,42],"paper,":[2],"authors":[4],"establish":[5],"a":[6],"general":[7],"inequality":[8,16],"for":[9],"hyperbolic":[11,30],"functions,":[12,19,32],"extend":[13],"newly-established":[15],"to":[17,37],"trigonometric":[18],"obtain":[20],"some":[21],"new":[22],"inequalities":[23,36],"involving":[24],"inverse":[26,29],"sine":[27,31],"and":[28,33,41],"apply":[34],"these":[35],"Neuman\u2013S\u00e1ndor":[39],"mean":[40],"first":[43],"Seiffert":[44],"mean.":[45]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}