Pointwise Estimates for the Coconvex Approximation of Differentiable Functions
- 19 Downloads
We obtain pointwise estimates for the coconvex approximation of functions of the class W r , r > 3.
KeywordsDifferentiable Function Pointwise Estimate Coconvex Approximation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 2.H. A. Dzyubenko and V. D. Zalizko, “Coconvex approximation of functions with more than one inflection point,” Ukr. Mat. Zh., 56, No.3, 352–365 (2004).Google Scholar
- 6.I. A. Shevchuk, Polynomial Approximation and Traces of Functions Continuous on a Segment [in Russian], Naukova Dumka, Kiev (1992).Google Scholar
- 7.A. S. Shvedov, “Orders of coapproximations of functions by algebraic polynomials,” Mat. Zametki, 30, 839–846 (1981).Google Scholar
- 8.X. Wu and S. P. Zhou, “A counterexample in comonotone approximation in L p space,” Colloq. Math., 64, 265–274 (1993).Google Scholar
- 9.I. A. Shevchuk, “Approximation of monotone functions by monotone polynomials,” Mat. Sb., 183, 63–78 (1992).Google Scholar
- 12.V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).Google Scholar
- 14.V. K. Dzyadyk, “On the constructive characteristic of functions satisfying the condition (Lip α (0 < α < 1)) on a finite segment of the real axis,” Izv. Akad. Nauk SSSR, Ser. Mat., 20, No.2, 623–642 (1956).Google Scholar
- 15.H. Whitney, “On functions with bounded nth differences,” J. Math. Pures Appl., 8, No.36, 67–95 (1957).Google Scholar
© Springer Science+Business Media, Inc. 2005