Literature cited
G. K. Lebed', “Some questions in the approximation of functions of one variable by algebraic polynomials,” Dokl. Akad. Nauk SSSR,118, No. 2, 239–242 (1958).
M. K. Potapov, “On the approximation of nonperiodic functions by algebraic polynomials,” Vestn, Mosk. Gos. Univ., No. 4, 14–25 (1960).
M. K. Potapov, “On the structural and constructive characterizations of certain classes of functions,” Tr. Mosk. Inst. Akad. Nauk SSSR,131, 211–231 (1974).
L. B. Kohdak, “On the approximation of nonperiodic functions by algebraic polynomials in the metric of Lp, 0 < p < 1,” in: Investigations on Modern Problems of Summation and Approximation and Their Applications [in Russian], Izd. Dnepropetr. Univ., Dnepropetrovsk (1977), pp. 35–38.
V. I. Ivanov, “Direct and inverse theorems of the theory of approximation in the metric of Lp for 0 < p < 1,” Mat. Zametki,18, No. 5, 641–658 (1975).
É. A. Storozhenko, “On the approximation by algebraic polynomials of functions of the class Lp, 0 < p < 1,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 3, 652–663 (1977).
É. A. Storozhenko and P. Osval'd, “The theorems of Jackson in the spaces Lp(Rk), 0 < p < 1,” Dokl. Akad. Nauk SSSR,229, No. 3, 554–557 (1976).
É. A. Storozhenko, V. G. Krotov, and P. Osval'd, “Direct and inverse of Jackson type in the spaces Lp, 0 < p < 1,” Mat. Sb.,98, 395–415 (1975).
Yu. A. Brudnyi, “Approximation of functions by algebraic polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 4, 780–787 (1968).
V. I. Ivanov, “Some inequalities for trigonometric polynomials and their derivatives in various metrics,” Mat. Zametki,18, No. 4, 489–498 (1975).
M. K. Potapov, “Some inequalities for polynomials and their derivatives,” Vestn. Mosk. Gos. Univ., Ser. Mat. Mekh., No. 2, 10–19 (1960).
A. F. Timan, The Theory of Approximation of Functions [in Russian], Fizmatgiz, Moscow (1960).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 423–431, May–June, 1980.
Rights and permissions
About this article
Cite this article
Khodak, L.B. Structural characteristics of some classes of functions in the metric of Lp for 0 < p < 1. Ukr Math J 32, 287–293 (1980). https://doi.org/10.1007/BF01089773
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01089773