References
E. W. Cheney,Introduction to approximation theory, McGraw-Hill (New York, 1966).
A. Kroó, The continuity of best aproximations,Acta Math. Acad. Sci. Hungar.,30 (1977), 175–188.
G. Freud, Eine Ungleichung für Tshebyscheffsche Approximationspolynome,Acta Sci. Math. Szeged,19 (1958), 162–164.
D. J. Newman, H. S. Shapiro, Some theorems on Čebysev approximation,Duke Math. J.,30 (1963), 673–681.
R. Holmes, B. Kripke, Smoothness of approximation,Mich. Math. J.,15 (1968), 225–248.
B. O. Björnestal, Continuity of the Metric Projection Operator I–III,The preprint series of Department of Mathematics, Royal Institute of Technology, Stockholm, TRITAMAT,17 (1974),20 (1974),12 (1975).
П. В. Галкин, О модуле непрерывности оператора наилучшего приближения в пространстве непрерывных функций,Мамем. замемки,10 (1971), 601–613.
А. В. Кроо, Задача корректности наилучших приближений тригонометрическими полиномами классаW r0 H[ω] c ,Мамем. замемки,22 (1977), 85–103.
J. R. Rice,The Approximation of Functions I, Addison-Wesley (1964).
H. S. Shapiro,Topics in Approximation Theory. Lecture Notes in Math. 187. Springer-Verlag (Berlin-Heidelberg-New York, 1971.)
C. R. Hobby, J. R. Rice, A moment problem in approximation,Proc. Amer. Math. Soc.,65 (1965), 665–670.
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Kroó, A. On the continuity of best approximations in the space of integrable functions. Acta Mathematica Academiae Scientiarum Hungaricae 32, 331–348 (1978). https://doi.org/10.1007/BF01902369
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DOI: https://doi.org/10.1007/BF01902369