{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:30:27Z","timestamp":1740137427955,"version":"3.37.3"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","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\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671271"],"award-info":[{"award-number":["11671271"]}],"id":[{"id":"10.13039\/501100001809","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":[[2020,7]]},"abstract":"<jats:p> This paper gives a kind of sharp simultaneous approximation error estimation of Birkhoff interpolation [Formula: see text], [Formula: see text] where [Formula: see text] and [Formula: see text] is the Birkhoff interpolation based on [Formula: see text] pairs of numbers [Formula: see text] with its P[Formula: see text]lya interpolation matrix to be regular. First, based on the integral remainder formula of Birkhoff interpolation, we refer the computation of [Formula: see text] to the norm of an integral operator. Second, we refer the values of [Formula: see text] and [Formula: see text] to two explicit integral expressions and the value of [Formula: see text] to the computation of the maximum eigenvalue of a Hilbert\u2013Schmidt operator. At the same time, we give the corresponding sharp Wirtinger inequality [Formula: see text] and sharp Picone inequality [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219691320500216","type":"journal-article","created":{"date-parts":[[2020,1,22]],"date-time":"2020-01-22T07:51:02Z","timestamp":1579679462000},"page":"2050021","source":"Crossref","is-referenced-by-count":4,"title":["Simultaneous approximation of Birkhoff interpolation and the associated sharp inequalities"],"prefix":"10.1142","volume":"18","author":[{"given":"Zehong","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanting","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Capital Normal University, Beijing 100048, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guiqiao","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,3,5]]},"reference":[{"doi-asserted-by":"publisher","key":"S0219691320500216BIB001","DOI":"10.4153\/CMB-2008-018-6"},{"key":"S0219691320500216BIB002","first-page":"1","volume":"46","author":"Aydin T.","year":"2014","journal-title":"Electron. J. Qual. Theory Differ. Equ."},{"doi-asserted-by":"publisher","key":"S0219691320500216BIB003","DOI":"10.1090\/S0002-9947-1906-1500736-1"},{"doi-asserted-by":"publisher","key":"S0219691320500216BIB004","DOI":"10.1142\/S0219199710003804"},{"key":"S0219691320500216BIB005","first-page":"387","volume":"6","author":"Jaro\u0161 J.","year":"2001","journal-title":"J. Inequal. 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