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oai:recercat.cat:2072/3776162024-12-20T11:01:35Zcom_2072_199267com_2072_4427col_2072_199862

Pointwise Estimates for $ 3$ -monotone Approximation Bondarenko, A. Leviatan, D. Prymak, A. Matemàtiques 51 We prove that for a $ 3$ -monotone function $ F\in C[-1,1]$ , one can achieve the pointwise estimates \[ |F(x)-\Psi(x)|\le c\omega_3(F,\rho_n(x)), \quad x\in[-1,1], \] where $ \rho_n(x):=\frac1{n^2}+\frac{\sqrt{1-x^2}}n$ and $ c$ is an absolute constant, both with $ \Psi$ , a $ 3$ -monotone quadratic spline on the $ n$ th Chebyshev partition, and with $ \Psi$ , a~$ 3$ -monotone polynomial of degree $ \le n$ . The basis for the construction of these splines and polynomials is the construction of $ 3$ -monotone splines, providing appropriate order of pointwise \linebreak approximation, half of which nodes are prescribed and the other half are free, but controlled'\'''\''. 2011-01-01 info:eu-repo/semantics/preprint http://hdl.handle.net/2072/377616 eng CRM Preprints L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess 31 p. application/pdf RECERCAT (Dipòsit de la Recerca de Catalunya)