caa a22 4500 475743695 CHVBK 20180406123506.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s003650010003 doi (NATIONALLICENCE)springer-10.1007/s003650010003 More on Comonotone Polynomial Approximation [Elektronische Daten] [D. Leviatan, I. A. Shevchuk] Abstract. : The main achievement of this paper is that we show, what was to us, a surprising conclusion, namely, twice continuously differentiable functions in (0,1) (with some regular behavior at the endpoints) which change monotonicity at least once in the interval, are approximable better by comonotone polynomials, than are such functions that are merely monotone. We obtain Jackson-type estimates for the comonotone polynomial approximation of such functions that are impossible to achieve for monotone approximation. Springer-Verlag New York, 2000 Key words. Comonotone approximation by polynomials, Degree of approximation. AMS Classification. 41A10, 41A25, 41A29 nationallicence Leviatan D. School of Mathematics Tel Aviv ,Israel, Raymond and Beverley Sackler Faculty of Exact Sciences Tel Aviv University 69978, IL aut Shevchuk I. A. Institute of Mathematics Kyiv Ukraine, National Academy of Sciences of Ukraine 3, Tereshchenkivska str. 252601, UA aut https://doi.org/10.1007/s003650010003 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003650010003 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Leviatan D. School of Mathematics Tel Aviv ,Israel, Raymond and Beverley Sackler Faculty of Exact Sciences Tel Aviv University 69978, IL aut NATIONALLICENCE 700 1- Shevchuk I. A. Institute of Mathematics Kyiv Ukraine, National Academy of Sciences of Ukraine 3, Tereshchenkivska str. 252601, UA aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer