[1] V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126 | DOI | MR | Zbl

[2] D. Braess, Nonlinear approximation theory, Springer, 1986 | MR | Zbl

[3] V. I. Burenkov, “Exact constants in inequalities for norms of intermediate derivatives on a finite interval. II”, Trudy Mat. Inst. Steklov, 173, 1986, 38–49 | MR | Zbl

[4] J. A. Clarkson, “Uniformly convex spaces”, Trans. Amer. Math. Soc., 40 (1936), 396–414 | DOI | MR | Zbl

[5] P. J. Davis, Interpolation and approximation, Blaisdell, Waltham, MA, 1963 | MR | Zbl

[6] M. M. Day, Normed linear spaces, Springer, Berlin, 1973 | MR | Zbl

[7] R. DeVore, The approximation of continuous functions by positive linear operators, Springer, Berlin, 1972 | MR | Zbl

[8] R. DeVore, G. G. Lorentz, Constructive approximation, Springer, Berlin, 1993 | MR | Zbl

[9] J. Diestel, J. J. Uhl, Vector measures, Amer. Math. Soc., 1977 | MR | Zbl

[10] P. Dodos, Banach spaces and descriptive set theory: Selected topics, Springer, Berlin, 2010 | MR | Zbl

[11] P. Enflo, “A counterexample to the approximation property in Banach spaces”, Acta Math., 130 (1973), 309–317 | DOI | MR | Zbl

[12] A. L. Garkavi, “On best approximation by the elements of infinite-dimensional subspaces of a certain class”, Sb. Math., 62(104):1 (1963), 104–120 | MR | Zbl

[13] A. L. Garkavi, “On Chebyshev and almost Chebyshev subspaces”, Izv. Akad. Nauk SSSR Ser. Mat., 28:4 (1964), 799–818 | MR | Zbl

[14] V. I. Ivanov, Introduction to Approximation Theory, Tula State. Univ., Tula, 1999 (in Russian)

[15] O. G. Jørsboe, L. Mejlbro, The Carleson–Hunt theorem on Fourier series, Springer, Berlin, 1982 | MR

[16] S. Ya. Havinson, Z. S. Romanova, “Approximation properties of finite-dimensional subspaces in $L^1$”, Sb. Math., 89(131):1(9) (1972), 3–15 | MR | Zbl

[17] A. N. Kolmogorov, Selected Works, ed. V. M. Tikhomirov, Kluwer, 1991 | Zbl

[18] A. N. Kolmogorov, “Une généralisation de l'inégalité de M. J. Hadamard entre les bornes supérieures des dérivées successives d'une fonction”, C. R. Acad. Sci. Paris, 207 (1938), 764–765 | Zbl

[19] N. P. Korneĭchuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156 | DOI | MR | Zbl

[20] N. P. Korneĭchuk, Splines in approximation theory, Nauka, Moscow, 1984 (in Russian) | MR

[21] N. P. Korneĭchuk, V. F. Babenko, A. A. Ligun, Extremal properties of polynomials and splines, Nova Science, New York, 1996 | MR | Zbl

[22] B. R. Kripke, T. J. Rivlin, “Approximations in the metric of $L^1(x,\mu)$”, Trans. Amer. Math. Soc., 119 (1965), 101–122 | MR | Zbl

[23] V. I. Krylov, Approximate calculation of integrals, Nauka, Moscow, 1967 ; Dover, New York, 2005 | MR | Zbl

[24] G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, New York, 1966 | MR | Zbl

[25] G. G. Lorentz, S. D. Riemenschneider, K. Jetter, Birkhoff interpolation, Addison-Wesley, Reading, Mass., 1983 | MR | Zbl

[26] V. A. Markov, Über Polynome die einen geyebenen Intervalle moglichst wenig von null abweichen, St. Petersburg, 1892; Math. Ann., 77 (1916), 213–258 | DOI | MR | Zbl

[27] G. Mastroianni, G. V. Milovanović, Interpolation processes Basic theory and applications, Springer, Berlin, 2008 | MR | Zbl

[28] R. Megginson, An introduction to Banach space theory, Springer, Berlin, 1998 | MR | Zbl

[29] D. P. Milman, “On some criteria for the regularity of spaces of the type $(B)$”, Dokl. Akad. Nauk SSSR (N.S.), 20 (1938), 243–246 | Zbl

[30] I. P. Natanson, Constructive function theory, v. I, Frederic Ungar, New York, 1964 | MR | Zbl

[31] I. P. Natanson, Constructive function theory, v. III, Frederic Ungar, New York, 1965 | Zbl

[32] S. M. Nikol'skii, “Sur certaines méthodes d'approximation au moyen de sommes trigonométriques”, Izv. Akad. Nauk SSSR Ser. Mat., 4:6 (1940), 509–520 | MR | Zbl

[33] G. Nürnberger, Approximation by splines, Springer, Berlin, 1989 | MR | Zbl

[34] B. J. Pettis, “A proof that every uniformly convex space is reflexive”, Duke Math. J., 5 (1939), 249–253 | DOI | MR | Zbl

[35] J. R. Rice, The approximation of functions, v. I, Linear theory, Addison-Weseley, Reading, Mass., 1964 | Zbl

[36] J. R. Rice, The approximation of functions, v. II, Nonlinear and multivariate theory, Addison-Weseley, Reading, Mass., 1969 | Zbl

[37] T. J. Rivlin, An introduction to the approximation of functions, Blaisdell, Waltham, MA, 1969 | MR | Zbl

[38] T. J. Rivlin, The Chebyshev polynomials, Wiley, New York, 1974 | MR | Zbl

[39] K. Scherer, “On Bernstein's inequalities in Banach space”, Math. Notes, 17:6 (1975), 925–937 | MR | Zbl

[40] H. S. Shapiro, Topics in approximation theory, Springer, Berlin, 1971 | MR | Zbl

[41] I. Singer, “Some remarks on approximative compactness”, Rev. Roumaine Math. Pures Appl., 9 (1964), 167–177 | MR | Zbl

[42] I. Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer, Berlin, 1970 | MR | Zbl

[43] I. Singer, The theory of best approximation and functional analysis, SIAM, Philadelphia, 1974 | MR | Zbl

[44] S. B. Stechkin, “Generalization of some inequalities of S. N. Bernstein”, Dokl. Math., 60 (1948), 1511–1514 | MR | Zbl

[45] A. I. Stepanets, Methods of approximation theory, Brill Academic Publ., 2005 | MR

[46] V. Tikhomirov, A. Kochurov, “Kolmogorov-type inequalities on the whole line or half line and the Lagrange principle in the theory of extremum problems”, Eurasian Math. J., 2:3 (2011), 125–142 | MR | Zbl

[47] A. F. Timan, Theory of approximation of functions of a reaf variable, Macmillan, New York, 1963 | MR

[48] V. A. Zalgaller, “$k$-dimensional directions which are singular for a convex body $F$ in $\mathbb R^n$”, Zap. Nauchn. Sem. LOMI, 27, 1972, 67–72 | MR | Zbl

[49] R. Webster, Convexity, Oxford University, Oxford, 1993 | MR

[50] E. T. Whittaker, G. N. Watson, A course of modern analysis, Cambridge, 1996 | MR