{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:39:46Z","timestamp":1771677586378,"version":"3.50.1"},"reference-count":16,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MFC"],"published-print":{"date-parts":[[2022]]},"abstract":"<p style='text-indent:20px;'>In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\tau(x), $\\end{document}<\/tex-math><\/inline-formula> where <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\tau $\\end{document}<\/tex-math><\/inline-formula> is infinitely differentiable function on <inline-formula><tex-math id=\"M3\">\\begin{document}$ [0, 1], \\; \\tau(0) = 0, \\tau(1) = 1 $\\end{document}<\/tex-math><\/inline-formula> and <inline-formula><tex-math id=\"M4\">\\begin{document}$ \\tau^{\\prime }(x)&gt;0, \\;\\forall\\;\\; x\\in[0, 1]. $\\end{document}<\/tex-math><\/inline-formula> We study the degree of approximation by means of the modulus of continuity and the Ditzian-Totik modulus of smoothness. A Voronovskaja type asymptotic theorem and the approximation of functions with derivatives of bounded variation are also studied. By means of a numerical example, finally we illustrate the convergence of these operators to certain functions through graphs and show a careful choice of the function <inline-formula><tex-math id=\"M5\">\\begin{document}$ \\tau(x) $\\end{document}<\/tex-math><\/inline-formula> leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [<xref ref-type=\"bibr\" rid=\"b11\">11<\/xref>].<\/p><\/jats:p>","DOI":"10.3934\/mfc.2021024","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T04:13:42Z","timestamp":1634703222000},"page":"75","source":"Crossref","is-referenced-by-count":3,"title":["Better degree of approximation by modified Bernstein-Durrmeyer type operators"],"prefix":"10.3934","volume":"5","author":[{"given":"Purshottam Narain","family":"Agrawal","sequence":"first","affiliation":[]},{"given":"\u015eule Y\u00fcksel","family":"G\u00fcng\u00f6r","sequence":"additional","affiliation":[]},{"given":"Abhishek","family":"Kumar","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/mfc.2021024-1","doi-asserted-by":"publisher","unstructured":"T. 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Deo et al.), Springer, \n(2020), 77-88.","DOI":"10.1007\/978-981-15-1153-0_7"},{"key":"key-10.3934\/mfc.2021024-5","doi-asserted-by":"publisher","unstructured":"P. N. Agrawal, N. Bhardwaj and P. Bawa, B\u00e9zier variant of modified $\\alpha$- Bernstein operators, Rend. Circ. Mat. Palermo, II Ser.<\/i>, (2021).","DOI":"10.1007\/s12215-021-00613-x"},{"key":"key-10.3934\/mfc.2021024-6","unstructured":"S. Bernstein.D\u00e9monstration du theor\u00e9me de Weierstrass fond\u00e9e sur le calcul des probabiliti\u00e9s, Comm. Kharkov Math. Soc.<\/i>, 13<\/b> (1912), 1-2."},{"key":"key-10.3934\/mfc.2021024-7","doi-asserted-by":"publisher","unstructured":"N. \u00c7etin, V. A. Radu.Approximation by generalized Bernstein-Stancu operators, Turk. J. Math.<\/i>, 43<\/b> (2019), 2032-2048.","DOI":"10.3906\/mat-1903-109"},{"key":"key-10.3934\/mfc.2021024-8","doi-asserted-by":"publisher","unstructured":"R. A. Devore and G. G. Lorentz, Constructive Approximation<\/i>, Grundlehren Math. 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