{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:12:19Z","timestamp":1760235139558,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,31]],"date-time":"2021-07-31T00:00:00Z","timestamp":1627689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Lucian Blaga University of Sibiu and Hasso Plattner Foundation","award":["LBUS-IRG-2020-06"],"award-info":[{"award-number":["LBUS-IRG-2020-06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We consider positive linear operators having the same fundamental functions and different functionals in front of them. For differences involving such operators, we obtain Voronovskaja-type quantitative results. Applications illustrating the theoretical aspects are presented.<\/jats:p>","DOI":"10.3390\/sym13081392","type":"journal-article","created":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T21:46:44Z","timestamp":1627854404000},"page":"1392","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Voronovskaja-Type Quantitative Results for Differences of Positive Linear Operators"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1192-2281","authenticated-orcid":false,"given":"Ana Maria","family":"Acu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5\u20137, 550012 Sibiu, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3216-1661","authenticated-orcid":false,"given":"G\u00fclen","family":"Ba\u015fcanbaz-Tunca","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ankara University, Str. D\u00f6gol, 06100 Ankara, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5206-030X","authenticated-orcid":false,"given":"Ioan","family":"Ra\u015fa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Str. Memorandumului No. 28, 400114 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,31]]},"reference":[{"key":"ref_1","unstructured":"M\u00fcller, M.W. (1995). The approximation by means of some linear positive operators. Approximation Theory, Akademie."},{"key":"ref_2","first-page":"113","article-title":"A Survey on Estimates for the Differences of Positive Linear Operators","volume":"1","author":"Acu","year":"2018","journal-title":"Constr. Math. Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1007\/s11075-016-0117-8","article-title":"New estimates for the differences of positive linear operators","volume":"73","author":"Acu","year":"2016","journal-title":"Numer. Algorithms"},{"key":"ref_4","first-page":"537544","article-title":"Discrete operators associated with certain integral operators","volume":"56","year":"2011","journal-title":"Stud. Univ. Babe\u015f Bolyai Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1007\/s13324-020-00423-x","article-title":"Discrete Operators associated with Linking Operators","volume":"10","author":"Heilmann","year":"2020","journal-title":"Anal. Math. Phys."},{"key":"ref_6","unstructured":"Voronovskaja, E. (1932). D\u00e9termination de la forme asymtotique d\u2019approximation des fonctions parles polyn\u00f4mes de M. Bernstein. C. R. Acad. Sci URSS, 79\u201385. Available online: https:\/\/scholar.google.com\/scholar_lookup?title=D%C3%A9termination+de+la+forme+asymptotique+d%27approximation+des+fonctions+par+les+polynomes+de+M.+Bernstein&author=Voronowskaja+E.&publication+year=1932&journal=C.+R.+Acad.+Sci.+U.R.S.S.&pages=79-85."},{"key":"ref_7","unstructured":"Videnski\u012d, V.S. (1985). Linear Positive Operators of Finite Rank (Russian), \u201cA.I. Gerzen\u201d State Pedagogical Institute."},{"key":"ref_8","first-page":"595","article-title":"Sur certains d\u00e9veloppements suivant les polyn\u00f4mes de la forme de S. Bernstein, I, II","volume":"563\u2013568","author":"Kantorovich","year":"1930","journal-title":"C. R. Acad. Sci. URSS"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/j.jmaa.2008.01.085","article-title":"Voronovskaja\u2019s theorem revisited","volume":"343","author":"Tachev","year":"2008","journal-title":"J. Math. Anal. Appl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/8\/1392\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:38:11Z","timestamp":1760164691000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/8\/1392"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,31]]},"references-count":9,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["sym13081392"],"URL":"https:\/\/doi.org\/10.3390\/sym13081392","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,7,31]]}}}