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Polynomial operators for one-sided approximation to functions in $W^r_p [0,1]$. (English) Zbl 1258.41003
Some operators for one-sided approximation of differentiable functions by algebraic polynomials in $L_p$ spaces are presented. The estimates for the error of approximation are given with an explicit constant. The approximation of differentiable functions is considered in this paper. The approximation of nondifferentiable functions will be considered in another paper.

41A10Approximation by polynomials
41A35Approximation by operators (in particular, by integral operators)
Full Text: DOI
[1] Jianli, W.; Songping, Z.: Some converse results on one-sided approximation: justifications, Anal. theory appl. 19, No. 3, 280-288 (2003) · Zbl 1054.41007 · doi:10.1007/BF02835287
[2] Motornyi, V. P.; Motornaya, O. V.; Nitiema, P. K.: One-sided approximation of a step by algebraic polynomials in the mean, Ukrainian math. J. 62, No. 3, 467-482 (2010) · Zbl 1224.41023 · doi:10.1007/s11253-010-0366-y
[3] Motornyi, V. P.; Pas’ko, A. N.: On the best one-sided approximation of some classes of differentiable functions in L1, East J. Approx. 10, No. 1--2, 159-169 (2004) · Zbl 1113.41009
[4] Taikov, L. V.: One-sided approximation of functions, Math. notes 67, No. 1, 108-111 (2000) · Zbl 0972.42001 · doi:10.1007/BF02675798
[5] V.H. Hristov, K.G. Ivanov, Operators for one-sided approximation of functions, in: Constructive Theory of Functions’87, Proc. Intern. Conference, Varna, Sofia 1988, pp. 222--232. · Zbl 0702.41008
[6] Hristov, V. H.; Ivanov, K. G.: Operators for one-sided approximation by algebraic polynomials in $Lp([-1,1]d)$, Math. balkanica (NS) 2, No. 4, 374-390 (1988) · Zbl 0669.41007
[7] Lenze, B.: Operators for one-sided approximation by algebraic polynomials, J. approx. Theory 54, 169-179 (1988) · Zbl 0674.41013 · doi:10.1016/0021-9045(88)90017-2
[8] Butzer, P. L.; Nessel, R. J.: Fourier analysis and approximation, Fourier analysis and approximation 1 (1971) · Zbl 0217.42603
[9] Bustamante, J.; Quesada, J. M.; Martínez-Cruz, R.: Best one-sided L1 approximation to the heaviside and sign functions, J. approx. Theory 164, No. 6, 791-802 (2012) · Zbl 1248.41013