Abstract
It is proved that the sets of extremal functions are massive in some problems in approximation theory.
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V. I. Ruban, “Interpolation of functions and their derivatives by the elements of subspaces in general position,” in:Investigation of the Modern Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1983), pp. 52–54.
E. A. Wickeren, “Baire approach to quantitative resonance principles,”Numer. Funct. Anal. Optimizat.,9, No. 1, 147–180 (1987).
E. B. Saff and V. Totik, “Behavior of polynomials of best uniform approximation,”Trans. Amer. Math. Soc.,316, No. 2, 567–590 (1989).
O. V. Davydov, “On the accuracy of Jackson-type and Lebesgue-type inequalities,” in:Approximation of Functions and Summation of Series [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1991), pp. 19–28.
H. Whitney, “On a function with boundedn th differences,”J. Math. Pure Appl., 67–95 (1967).
M. I. Kadei, “On the distribution of the maximal deviation points under approximation of continuous functions by polynomials,”Usp. Mat. Nauk,15, Issue 1 (91), 199–202 (1960).
N. P. Korneichuk, “The exact constant in Jackson's theorem on the best uniform approximation of continuous periodic functions,”Dokl. Akad. Nauk SSSR,145, No. 3, 514–515 (1962).
A. A. Ligun, “Exact constants of the approximation of differentiable periodic functions,”Mat. Zametki,14, No. 1, 21–30 (1973).
N. I. Chernykh, “On Jackson's inequalities inL 2,”Tr. Mat. Inst. Akad. Nauk SSSR,88, 71–74 (1967).
N. P. Korneichuk, “Exact constant in Jackson's inequality for continuous periodic functions,”Mat. Zametki,32, No. 5, 669–774 (1982).
A. A. Ligun, “Inequalities for upper bounds of functions,”Anal. Math.,2, No. 1, 11–40 (1976).
N. P. Korneichuk, “Inequalities for the best approximation of differentiable periodic functions by splines,”Ukr. Mat. Zh.,31, No. 4, 380–388 (1979).
V. T. Gavrilyuk and. S. B. Stechkin, “Approximation of continuous periodic functions by Fourier sums,”Tr. Mat. Inst. Akad. Nauk SSSR,172, 107–127 (1985).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1356–1361, October, 1993.
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Kofanov, V.A. Massiveness of the sets of extremal functions in some problems in approximation theory. Ukr Math J 45, 1520–1527 (1993). https://doi.org/10.1007/BF01571086
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DOI: https://doi.org/10.1007/BF01571086