{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:25:13Z","timestamp":1753881913486,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871006"],"award-info":[{"award-number":["11871006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007847","name":"Natural Science Foundation of Jilin Province","doi-asserted-by":"publisher","award":["11671271"],"award-info":[{"award-number":["11671271"]}],"id":[{"id":"10.13039\/100007847","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p> This study gives a kind of sharp Wirtinger inequalities (Pizone inequalities) [Formula: see text] where [Formula: see text] with at least [Formula: see text] zeros (counting multiplicity) in [Formula: see text]. First, based on the Hermite (Lagrange) interpolation, we express [Formula: see text] as a Lagrange type (integral type) remainder. Second, we refer the computation of [Formula: see text] to the maximum value problem of a multivariate function, and we give the values of [Formula: see text] by finding the solution of the multivariate function aforementioned. At last, we refer the computation of [Formula: see text] to the norm of an integral operator. Our results are corrections and extensions to the results that appear in [J. C. Kuang, Applied Inequalities (Shandong Science and Technology Press, Jinan, 2004); A. Yu. Levin, Some estimates for a diff erentiable function, Dokl. Akad. Nauk SSSR 138 (1961) 37-38 (in Russian)]. <\/jats:p>","DOI":"10.1142\/s0219691323500364","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T13:55:13Z","timestamp":1689083713000},"source":"Crossref","is-referenced-by-count":0,"title":["A kind of sharp Wirtinger inequalities"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1448-2963","authenticated-orcid":false,"given":"Guiqiao","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Tianjin Normal University, No. 393, Extension of Bin Shui West Road, Tianjin 300387, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongping","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Normal University, No. 19, Xinjiekouwai St Beijing 100875, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dandan","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Normal University, No. 19, Xinjiekouwai St Beijing 100875, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,8,2]]},"reference":[{"key":"S0219691323500364BIB001","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1090\/S0002-9947-1906-1500736-1","volume":"7","author":"Birkhoff G. D.","year":"1906","journal-title":"Trans. Amer. Math. Soc."},{"volume-title":"Applied Inequalities","year":"2004","author":"Kuang J. C.","key":"S0219691323500364BIB002"},{"key":"S0219691323500364BIB003","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.jat.2015.08.007","volume":"201","author":"Kuo F. Y.","year":"2016","journal-title":"J. Approx. Theory"},{"key":"S0219691323500364BIB004","first-page":"37","volume":"138","author":"Levin A. Yu.","year":"1961","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"4","key":"S0219691323500364BIB005","doi-asserted-by":"crossref","first-page":"2050021","DOI":"10.1142\/S0219691320500216","volume":"18","author":"Liu Z. H.","year":"2020","journal-title":"Int. J. Wavelets Multiresolut. Inf. Process."},{"key":"S0219691323500364BIB006","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1186\/s13660-019-2121-8","volume":"2019","author":"Xu G. Q.","year":"2019","journal-title":"J. Inequal. Appl."},{"issue":"1","key":"S0219691323500364BIB007","first-page":"347","volume":"51","author":"Xu G. Q.","year":"2021","journal-title":"Rocky Mt. J. Math."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691323500364","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T11:35:27Z","timestamp":1698838527000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691323500364"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,2]]},"references-count":7,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["10.1142\/S0219691323500364"],"URL":"https:\/\/doi.org\/10.1142\/s0219691323500364","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2023,8,2]]},"article-number":"2350036"}}