{"id":"https://openalex.org/W2014263347","doi":"https://doi.org/10.1155/2013/978493","title":"Refinements on the Hermite-Hadamard Inequalities for<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:math>-Convex Functions","display_name":"Refinements on the Hermite-Hadamard Inequalities for<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:math>-Convex Functions","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2014263347","doi":"https://doi.org/10.1155/2013/978493","mag":"2014263347"},"language":"lv","primary_location":{"id":"doi:10.1155/2013/978493","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/978493","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/978493.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/978493.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043380271","display_name":"Feixiang Chen","orcid":"https://orcid.org/0000-0002-1472-3678"},"institutions":[{"id":"https://openalex.org/I50180762","display_name":"Chongqing Three Gorges University","ror":"https://ror.org/05rs3pv16","country_code":"CN","type":"education","lineage":["https://openalex.org/I50180762"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Feixiang Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404000, China"],"raw_orcid":"https://orcid.org/0000-0002-1472-3678","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404000, China","institution_ids":["https://openalex.org/I50180762"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101730836","display_name":"Xuefei Liu","orcid":"https://orcid.org/0000-0003-0154-474X"},"institutions":[{"id":"https://openalex.org/I50180762","display_name":"Chongqing Three Gorges University","ror":"https://ror.org/05rs3pv16","country_code":"CN","type":"education","lineage":["https://openalex.org/I50180762"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuefei Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404000, China","institution_ids":["https://openalex.org/I50180762"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043380271"],"corresponding_institution_ids":["https://openalex.org/I50180762"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.8513,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.70912744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"5"},"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":0.9253000020980835,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9042999744415283,"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/mathematics","display_name":"Mathematics","score":0.609351634979248},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.49109363555908203},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4578172266483307},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3921720087528229},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32230889797210693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07519370317459106},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04565301537513733}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.609351634979248},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.49109363555908203},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4578172266483307},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3921720087528229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32230889797210693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07519370317459106},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04565301537513733}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/978493","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/978493","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/978493.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808135","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808135","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:9e76d53596c2429cbcf47fdad23dfabd","is_oa":true,"landing_page_url":"https://doaj.org/article/9e76d53596c2429cbcf47fdad23dfabd","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":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/978493","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/978493","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/978493.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5600000023841858}],"awards":[{"id":"https://openalex.org/G615653300","display_name":null,"funder_award_id":"cstc2012jjA00013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321546","display_name":"China Three Gorges University","ror":"https://ror.org/0419nfc77"},{"id":"https://openalex.org/F4320321550","display_name":"Chongqing Science and Technology Commission","ror":"https://ror.org/05w9erc61"},{"id":"https://openalex.org/F4320330197","display_name":"Chongqing Three Gorges University","ror":"https://ror.org/05rs3pv16"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2014263347.pdf","grobid_xml":"https://content.openalex.org/works/W2014263347.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1973926142","https://openalex.org/W1981491042","https://openalex.org/W1982716237","https://openalex.org/W1990485388","https://openalex.org/W2038244498","https://openalex.org/W2064832754","https://openalex.org/W2097184643","https://openalex.org/W2116225090","https://openalex.org/W2312257908","https://openalex.org/W2312358319","https://openalex.org/W2317162280","https://openalex.org/W2325583116"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W1982241170","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2386549147","https://openalex.org/W4225152035","https://openalex.org/W1978051046","https://openalex.org/W2061531152"],"abstract_inverted_index":{"We":[0],"give":[1],"some":[2],"new":[3],"generalizations":[4],"of":[5],"the":[6],"well-known":[7],"Hermite-Hadamard":[8],"inequality":[9],"for<mml:math":[10],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11],"id=\"M2\"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:math>-convex":[12],"functions.":[13]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
