{"id":"https://openalex.org/W4390348339","doi":"https://doi.org/10.3390/axioms13010021","title":"Improvements of Integral Majorization Inequality with Applications to Divergences","display_name":"Improvements of Integral Majorization Inequality with Applications to Divergences","publication_year":2023,"publication_date":"2023-12-28","ids":{"openalex":"https://openalex.org/W4390348339","doi":"https://doi.org/10.3390/axioms13010021"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13010021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010021","pdf_url":"https://www.mdpi.com/2075-1680/13/1/21/pdf?version=1703776797","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/2075-1680/13/1/21/pdf?version=1703776797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112530310","display_name":"Abdul Basir","orcid":null},"institutions":[{"id":"https://openalex.org/I36001604","display_name":"University of Peshawar","ror":"https://ror.org/02t2qwf81","country_code":"PK","type":"education","lineage":["https://openalex.org/I36001604"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Abdul Basir","raw_affiliation_strings":["Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I36001604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057057760","display_name":"Muhammad Adil Khan","orcid":"https://orcid.org/0000-0001-5373-4663"},"institutions":[{"id":"https://openalex.org/I36001604","display_name":"University of Peshawar","ror":"https://ror.org/02t2qwf81","country_code":"PK","type":"education","lineage":["https://openalex.org/I36001604"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Adil Khan","raw_affiliation_strings":["Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5373-4663","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I36001604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001945756","display_name":"Hidayat Ullah","orcid":"https://orcid.org/0000-0001-9428-2624"},"institutions":[{"id":"https://openalex.org/I36001604","display_name":"University of Peshawar","ror":"https://ror.org/02t2qwf81","country_code":"PK","type":"education","lineage":["https://openalex.org/I36001604"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Hidayat Ullah","raw_affiliation_strings":["Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I36001604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019236955","display_name":"Yahya Almalki","orcid":"https://orcid.org/0000-0003-1149-9559"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Yahya Almalki","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1149-9559","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007426245","display_name":"Chanisara Metpattarahiran","orcid":null},"institutions":[{"id":"https://openalex.org/I4210097440","display_name":"Suan Dusit University","ror":"https://ror.org/00x7vzk16","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210097440"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Chanisara Metpattarahiran","raw_affiliation_strings":["Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand","institution_ids":["https://openalex.org/I4210097440"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065323596","display_name":"Thanin Sitthiwirattham","orcid":"https://orcid.org/0000-0002-8455-1402"},"institutions":[{"id":"https://openalex.org/I4210097440","display_name":"Suan Dusit University","ror":"https://ror.org/00x7vzk16","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210097440"]},{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Thanin Sitthiwirattham","raw_affiliation_strings":["Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand","Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-8455-1402","affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand","institution_ids":["https://openalex.org/I4210097440"]},{"raw_affiliation_string":"Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5007426245","https://openalex.org/A5057057760"],"corresponding_institution_ids":["https://openalex.org/I36001604","https://openalex.org/I4210097440"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.5262,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82910542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"13","issue":"1","first_page":"21","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9697999954223633,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9559999704360962,"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/majorization","display_name":"Majorization","score":0.955022931098938},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.8300596475601196},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.6399270296096802},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5548572540283203},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5069403648376465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42844194173812866},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3377585709095001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33717650175094604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12972480058670044},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1077694296836853},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0851486325263977}],"concepts":[{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.955022931098938},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.8300596475601196},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.6399270296096802},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5548572540283203},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5069403648376465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42844194173812866},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3377585709095001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33717650175094604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12972480058670044},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1077694296836853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0851486325263977},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13010021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010021","pdf_url":"https://www.mdpi.com/2075-1680/13/1/21/pdf?version=1703776797","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:304fd30c69a84d52bfdd5e5e48b31f8c","is_oa":true,"landing_page_url":"https://doaj.org/article/304fd30c69a84d52bfdd5e5e48b31f8c","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":"Axioms, Vol 13, Iss 1, p 21 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13010021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010021","pdf_url":"https://www.mdpi.com/2075-1680/13/1/21/pdf?version=1703776797","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":0.4699999988079071,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390348339.pdf"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W153356541","https://openalex.org/W1980678487","https://openalex.org/W1983078831","https://openalex.org/W1985370657","https://openalex.org/W1987113198","https://openalex.org/W1991856940","https://openalex.org/W2029592138","https://openalex.org/W2032387672","https://openalex.org/W2032712686","https://openalex.org/W2034665207","https://openalex.org/W2036214360","https://openalex.org/W2039878365","https://openalex.org/W2069489937","https://openalex.org/W2078261139","https://openalex.org/W2115139092","https://openalex.org/W2328661291","https://openalex.org/W2335255444","https://openalex.org/W2603194489","https://openalex.org/W2898825750","https://openalex.org/W2923153527","https://openalex.org/W2942747238","https://openalex.org/W2990568942","https://openalex.org/W2997932628","https://openalex.org/W3006934234","https://openalex.org/W3027569370","https://openalex.org/W3027843755","https://openalex.org/W3044006605","https://openalex.org/W3102902904","https://openalex.org/W3105962170","https://openalex.org/W3120050151","https://openalex.org/W3135084800","https://openalex.org/W3173350212","https://openalex.org/W3175091319","https://openalex.org/W4200119807","https://openalex.org/W4206144597","https://openalex.org/W4210808694","https://openalex.org/W4223614392","https://openalex.org/W4229706427","https://openalex.org/W4255333822","https://openalex.org/W4300503237","https://openalex.org/W4309778145","https://openalex.org/W4381165441","https://openalex.org/W4386837896","https://openalex.org/W6606180642","https://openalex.org/W6659212356","https://openalex.org/W6735588220","https://openalex.org/W6774775957","https://openalex.org/W6786486187","https://openalex.org/W6788059893","https://openalex.org/W6791566335","https://openalex.org/W6806425538"],"related_works":["https://openalex.org/W371413493","https://openalex.org/W1988514170","https://openalex.org/W4320039931","https://openalex.org/W4214702501","https://openalex.org/W2050374035","https://openalex.org/W2524413221","https://openalex.org/W4313303878","https://openalex.org/W1932856329","https://openalex.org/W2033088280","https://openalex.org/W4246164825"],"abstract_inverted_index":{"Within":[0],"the":[1,44,59,66,72,83,90],"recent":[2],"wave":[3],"of":[4,65,82],"research":[5,36],"advancements,":[6],"mathematical":[7],"inequalities":[8,24,47],"and":[9,32,75,102],"their":[10],"practical":[11],"applications":[12,81],"play":[13],"a":[14,26],"notably":[15],"significant":[16],"role":[17],"across":[18],"various":[19],"domains.":[20],"In":[21],"this":[22],"regard,":[23],"offer":[25,93],"captivating":[27],"arena":[28],"for":[29,43,58,71,96],"scholarly":[30],"endeavors":[31],"investigational":[33],"pursuits.":[34],"This":[35],"work":[37],"aims":[38],"to":[39],"present":[40],"new":[41],"improvements":[42,54],"integral":[45],"majorization":[46,97],"using":[48],"an":[49],"interesting":[50],"aproach.":[51],"Certain":[52],"previous":[53],"have":[55],"been":[56],"achieved":[57],"Jensen":[60],"inequality":[61],"as":[62,80],"direct":[63],"outcomes":[64,92],"main":[67,84],"results.":[68,85],"Additionally,":[69],"estimates":[70],"Csisz\u00e1r":[73],"divergence":[74],"its":[76],"cases":[77],"are":[78,99],"provided":[79],"The":[86],"circumstances":[87],"under":[88],"which":[89],"principal":[91],"enhanced":[94],"estimations":[95],"differences":[98],"also":[100],"underscored":[101],"emphasized.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
