Literature Cited
S. M. Nikol'skii, “On the best approximation of functions satisfying a Lipschitz condition,” Izv. Akad. Nauk SSSR, Ser. Matem.,10, No. 2, 295–317 (1946).
Yu. A. Brudnyi, “Generalization of a theorem of A. F. Timan,” Dokl. Akad. Nauk SSSR,148, No. 6, 1237–1240 (1963).
A. F. Timan, “Strengthening of a theorem of Jackson,” Dokl. Akad. Nauk SSSR,81, No. 4, 509–511 (1951).
V. K. Dzyadyk, “On the approximation of functions by ordinary polynomials on a finite interval of the real axis,” Izv. Akad. Nauk SSSR, Ser. Matem.,22, No. 3, 337–354 (1958).
Frend, “Uber die Approximation reeller stetigen Functionen durch gewöhnliche Polynome,” Math. Ann.,137, No. 1, 17–25 (1959).
G. K. Lebed', “Some questions of approximation of functions of one variable by algebraic polynomials,” Dokl. Akad. Nauk SSSR,118, No. 2, 239–242 (1958).
M. K. Potapov, On Approximation in ℒp by algebraic polynomials. Analyses of Contemporary Problems of Constructive Function Theory [in Russian], Fizmatgiz, Moscow (1961), pp. 64–69.
V. P. Motornyi, “Some questions of approximation in an integral metric by algebraic polynomials,” Dokl. Akad. Nauk SSSR,172, No. 3, 537–540 (1967).
A. F. Timan, Theory of Approximation of Functions [in Russian], Fizmatgiz, Moscow (1960).
Yu. A. Brudnyi, Analyses in the Theory of Locally Best Approximation of Functions by Polynomials [in Russian], Dissertation, Dnepropetrovsk (1965).
Yu. A. Brudnyi, “Approximation of functions by algebraic polynomials,” Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 4, 780–787 (1968).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 13, No. 3, pp. 679, May–June, 1972.
Rights and permissions
About this article
Cite this article
Shalashova, L.Y. Mean approximation of functions on a finite interval. Sib Math J 13, 467–473 (1972). https://doi.org/10.1007/BF00968125
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968125