{"id":"https://openalex.org/W2036024161","doi":"https://doi.org/10.1155/2012/871845","title":"Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications","display_name":"Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2036024161","doi":"https://doi.org/10.1155/2012/871845","mag":"2036024161"},"language":"en","primary_location":{"id":"doi:10.1155/2012/871845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/871845","pdf_url":null,"source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1155/2012/871845","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112716122","display_name":"Lokenath Debnath","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lokenath Debnath","raw_affiliation_strings":["Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100674358","display_name":"Bicheng Yang","orcid":"https://orcid.org/0000-0002-9417-3310"},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I32246829","display_name":"Guangdong University of Education","ror":"https://ror.org/0574der91","country_code":"CN","type":"education","lineage":["https://openalex.org/I32246829"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bicheng Yang","raw_affiliation_strings":["Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China","Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, 510303, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China","institution_ids":["https://openalex.org/I32246829"]},{"raw_affiliation_string":"Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, 510303, China","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I32246829"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":3.7296,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.92767204,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"29"},"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":0.9186999797821045,"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":0.90829998254776,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8589504361152649},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5038992762565613},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.49775341153144836},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.46639177203178406},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.43342119455337524},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.42835038900375366},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.4189450740814209},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.4179891347885132},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.41461434960365295},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41359835863113403},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37487271428108215},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3505082130432129},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3398261070251465},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29030489921569824},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07357534766197205}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8589504361152649},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5038992762565613},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.49775341153144836},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46639177203178406},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.43342119455337524},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.42835038900375366},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.4189450740814209},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.4179891347885132},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.41461434960365295},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41359835863113403},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37487271428108215},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3505082130432129},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3398261070251465},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29030489921569824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07357534766197205},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/871845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/871845","pdf_url":null,"source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:871845","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/871845.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:1d453eceafe64e3a801b951f36bac7dd","is_oa":false,"landing_page_url":"https://doaj.org/article/1d453eceafe64e3a801b951f36bac7dd","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/871845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/871845","pdf_url":null,"source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G7102179524","display_name":null,"funder_award_id":"7004344","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":102,"referenced_works":["https://openalex.org/W28713162","https://openalex.org/W41480799","https://openalex.org/W77064137","https://openalex.org/W104279468","https://openalex.org/W134110372","https://openalex.org/W573176839","https://openalex.org/W937691225","https://openalex.org/W1003775798","https://openalex.org/W1486463879","https://openalex.org/W1511155450","https://openalex.org/W1574466347","https://openalex.org/W1577499129","https://openalex.org/W1605365976","https://openalex.org/W1651788694","https://openalex.org/W1678167890","https://openalex.org/W1968579208","https://openalex.org/W1969629913","https://openalex.org/W1975398841","https://openalex.org/W1977657677","https://openalex.org/W1980532636","https://openalex.org/W1981427948","https://openalex.org/W1986271469","https://openalex.org/W1989777868","https://openalex.org/W1992904096","https://openalex.org/W1994518041","https://openalex.org/W1997588345","https://openalex.org/W2000348367","https://openalex.org/W2003710178","https://openalex.org/W2007993212","https://openalex.org/W2009679807","https://openalex.org/W2017740159","https://openalex.org/W2017761485","https://openalex.org/W2019099917","https://openalex.org/W2019185376","https://openalex.org/W2020775429","https://openalex.org/W2022421046","https://openalex.org/W2031752698","https://openalex.org/W2038931748","https://openalex.org/W2039165395","https://openalex.org/W2042874189","https://openalex.org/W2045789458","https://openalex.org/W2047125067","https://openalex.org/W2048788200","https://openalex.org/W2070911304","https://openalex.org/W2077336946","https://openalex.org/W2090922263","https://openalex.org/W2096818832","https://openalex.org/W2097832657","https://openalex.org/W2102129414","https://openalex.org/W2103936127","https://openalex.org/W2104279625","https://openalex.org/W2114955259","https://openalex.org/W2116311617","https://openalex.org/W2130720360","https://openalex.org/W2131858072","https://openalex.org/W2138828655","https://openalex.org/W2144137822","https://openalex.org/W2161801459","https://openalex.org/W2163643881","https://openalex.org/W2171206339","https://openalex.org/W2181806288","https://openalex.org/W2183307530","https://openalex.org/W2185891794","https://openalex.org/W2189472879","https://openalex.org/W2314471702","https://openalex.org/W2316465892","https://openalex.org/W2319188592","https://openalex.org/W2319572282","https://openalex.org/W2328250190","https://openalex.org/W2330353449","https://openalex.org/W2330613698","https://openalex.org/W2330944852","https://openalex.org/W2333537478","https://openalex.org/W2337415853","https://openalex.org/W2349052204","https://openalex.org/W2349955976","https://openalex.org/W2351089872","https://openalex.org/W2353974789","https://openalex.org/W2354123284","https://openalex.org/W2356201900","https://openalex.org/W2356463495","https://openalex.org/W2357579013","https://openalex.org/W2362604466","https://openalex.org/W2367194416","https://openalex.org/W2367564984","https://openalex.org/W2369295830","https://openalex.org/W2371969820","https://openalex.org/W2374468577","https://openalex.org/W2376935492","https://openalex.org/W2378652546","https://openalex.org/W2380882876","https://openalex.org/W2384125022","https://openalex.org/W2386903924","https://openalex.org/W2390073620","https://openalex.org/W2390422280","https://openalex.org/W2392938828","https://openalex.org/W2412873325","https://openalex.org/W2511377927","https://openalex.org/W2806504701","https://openalex.org/W3140141232","https://openalex.org/W4243965246","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W634571496","https://openalex.org/W579400037","https://openalex.org/W2951578208","https://openalex.org/W1570037808","https://openalex.org/W4298173607","https://openalex.org/W3020816813","https://openalex.org/W4386784405","https://openalex.org/W115184939","https://openalex.org/W4285286257","https://openalex.org/W2952417038"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,52,86],"recent":[4,96],"developments":[5],"of":[6,26,81,92],"Hilbert-type":[7,27,82],"discrete":[8],"and":[9,17,24,42,49,63,95,111],"integral":[10],"inequalities":[11,28,62,73,83],"by":[12],"introducing":[13],"kernels,":[14],"weight":[15],"functions,":[16],"multiparameters.":[18],"Included":[19],"are":[20,74,84,102],"numerous":[21,87],"generalizations,":[22],"extensions,":[23],"refinements":[25],"involving":[29],"many":[30,53,60],"special":[31],"functions":[32,41,51],"such":[33],"as":[34],"beta,":[35],"gamma,":[36],"logarithm,":[37],"trigonometric,":[38],"hyper-bolic,":[39],"Bernoulli's":[40,43],"numbers,":[44],"Euler's":[45],"constant,":[46],"zeta":[47],"function,":[48],"hypergeometric":[50],"applications.":[54,88],"Special":[55],"attention":[56],"is":[57],"given":[58],"to":[59,64,104],"equivalent":[61],"conditions":[65],"under":[66],"which":[67],"the":[68,75],"constant":[69],"factors":[70],"involved":[71],"in":[72,108],"best":[76],"possible.":[77],"Many":[78],"particular":[79],"cases":[80],"presented":[85],"A":[89],"large":[90],"number":[91],"major":[93],"books":[94],"research":[97],"papers":[98],"published":[99],"during":[100],"2009\u20132012":[101],"included":[103],"stimulate":[105],"new":[106],"interest":[107],"future":[109],"study":[110],"research.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
