Positive linear operators with equidistant nodes

New Results on Rational Approximation

“…Estimate (7)-which holds in particular if m 1 = n and m 2 = s > 2, i.e. for S n operator-shows the pointwise approximation power of Shepard operators based on equispaced nodes in terms of ω and expresses interpolation condition not only at the endpoints, but at all the knots, therefore it gives a positive answer in some senses to a problem posed by Gavrea, Gonska and Kacsó in [9]. Such result confirms that the approximation power of such simple operators is in some senses stronger than by polynomials (cfr.…”

“…Saturation results are handled by Theorem 3. The novelty is Theorem 4 giving the first asymptotic relations of Voronovskaya-type for such Shepard-type operators and estimate (7) giving a positive answer in some senses to a problem posed by Gavrea, Gonska and Kacsó in [9] on the pointwise approximation power of linear operators on equidistant nodes. Grüss-type inequalities are also showed in Corollaries 1, 2 and 3.…”

Quantitative estimates for some modified Bernstein-Stancu operators

“…Gonska and D.P. Kacso [16], [17], O. Dogru [14], U. Abel, M. Ivan, R. Pȃltȃnea [1] and Y. Kageyama [18].…”