caa a22 4500 475743733 CHVBK 20180406123507.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s003650010008 doi (NATIONALLICENCE)springer-10.1007/s003650010008 Interpolatory Pointwise Estimates for Polynomial Approximation [Elektronische Daten] [H. H. Gonska, D. Leviatan, I. A. Shevchuk, H. -J. Wenz] Abstract. : We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f∈ C[0,1] , by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases. Springer-Verlag New York, 2000 Key words. Approximation by polynomials, Shape-preserving approximation, Degree of approximation, Interpolatory pointwise estimates. AMS Classification. 41A10, 41A25, 41A29 nationallicence Gonska H. H. Fachbereich Mathematik gonska@informatik.uni-duisburg.de, Universität Duisburg 47048 Duisburg Germany, DE aut Leviatan D. School of Mathematical Sciences Israel leviatan@math.tau.ac.il, Sackler Faculty of Exact Sciences Tel Aviv University Tel Aviv 69978, IL aut Shevchuk I. A. Faculty of Mathematics and Mechanics shevchuk@imath.kiev.ua, National Taras Shevchenko University of Kyiv 252017 Kyiv Ukraine, UA aut -J. Wenz H. Fachbereich Mathematik, wenz@informatik.uni-duisburg.de, Universität Duisburg 47048 Duisburg Germany, DE aut https://doi.org/10.1007/s003650010008 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003650010008 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gonska H. H. Fachbereich Mathematik gonska@informatik.uni-duisburg.de, Universität Duisburg 47048 Duisburg Germany, DE aut NATIONALLICENCE 700 1- Leviatan D. School of Mathematical Sciences Israel leviatan@math.tau.ac.il, Sackler Faculty of Exact Sciences Tel Aviv University Tel Aviv 69978, IL aut NATIONALLICENCE 700 1- Shevchuk I. A. Faculty of Mathematics and Mechanics shevchuk@imath.kiev.ua, National Taras Shevchenko University of Kyiv 252017 Kyiv Ukraine, UA aut NATIONALLICENCE 700 1- -J. Wenz H. Fachbereich Mathematik, wenz@informatik.uni-duisburg.de, Universität Duisburg 47048 Duisburg Germany, DE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer