Citation: |
[1] |
C. K. Chui and P. W. Smith, A note on Landau's problem for bounded intervals, Amer. Math. Monthly, 82 (1975), 927-929.doi: 10.2307/2318501. |
[2] |
P. Erdös and G. Szegö, On a problem of I. Schur, Ann. of Math. (2), 43 (1942), 451-470.doi: 10.2307/1968803. |
[3] |
B.-O. Eriksson, Some best constants in the Landau inequality on a finite interval, J. Approx. Theory, 94 (1998), 420-454.doi: 10.1006/jath.1998.3203. |
[4] |
M. Floater, Error formulas for divided difference expansions and numerical differentiation, J. Approx. Theory, 122 (2003), 1-9.doi: 10.1016/S0021-9045(03)00025-X. |
[5] |
S. Karlin, Oscillatory perfect splines and related extremal problems, in "Studies in Spline Functions and Approximation Theory", 371-460. Academic Press, New York, (1976). |
[6] |
E. Landau, Einige Ungleichungen für zweimal differenzierbare Funktionen, Proc. London Math. Soc., 13 (1914), 43-39.doi: 10.1112/plms/s2-13.1.43. |
[7] |
A. P. Matorin, On inequalities between the maxima of the absolute values of a function and its derivatives on a half-line, Ukrain. Mat. Zh., 7 (1955), 262-266 = Amer. Math. Soc. Transl. (2), 8 (1958), 13-17. |
[8] |
N. Naidenov, On an extremal problem of Kolmogorov type for functions from $W^4_\infty$([a,b]), East J. Approx., 9 (2003), 117-135. |
[9] |
A. Pinkus, Some extremal properties of perfect splines and the pointwise Landau problem on the finite interval, J. Approx. Theory, 23 (1978), 37-64.doi: 10.1016/0021-9045(78)90077-1. |
[10] |
M. Sato, The Landau inequality for bounded intervals with $f^{(3)}$ finite, J. Approx. Theory, 34 (1982), 159-166.doi: 10.1016/0021-9045(82)90089-2. |
[11] |
I. Schur, Über das Maximum des absoluten Betrages eines Polynoms in einem gegebenen Intervall, Math. Z., 4 (1919), 271-287.doi: 10.1007/BF01203015. |
[12] |
A. Shadrin, Interpolation with Lagrange polynomials. A simple proof of Markov inequality and some of its generalizations, Approx. Theory Appl., 8 (1992), 51-61. |
[13] |
A. Shadrin, To the Landau-Kolmogorov problem on a finite interval, in "Open Problems in Approximation Theory" (Ed. B. Bojanov), 192-204, SCT Publishing, Singapore, (1994). |
[14] |
A. Shadrin, Error bounds for Lagrange interpolation, J. Approx. Theory, 80 (1995), 25-49.doi: 10.1006/jath.1995.1003. |
[15] |
A. Shadrin, Twelve proofs of the Markov inequality, in "Approximation Theory: A Volume Dedicated to Borislav Bojanov" (Eds. G. Nikolov et al), 233-298, Prof. M. Drinov Acad. Publ. House, Sofia, (2004). |
[16] |
A. I. Zvyagintsev, Kolmogorov's inequalities for $n=4$, Latv. Mat. Ezhegodnik, 26 (1982), 165-175 (in Russian). |
[17] |
A. I. Zvyagintsev and A. Ya. Lepin, Kolmogorov's inequalities between the upper bounds of derivatives of functions for $n=3$, Latv. Mat. Ezhegodnik, 26 (1982), 176-181 (in Russian). |