Some Global Direct Estimates for Kantorovitch Polynomials

Abstract

Improving a result of Hoeffding 1971, it is shown that l/x(l-x)/(x)eBK[0, 1] implies the rate for the approximation by Kantorovitch polynomials in L'.

Approximation Strategy by Positive Linear Operators

“…which has been studied most widely among the positive linear operators of the form (2) (see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]). Interested readers could also refer to the related papers for the other similar operators.…”

“…Corollary 18. Given ( ) ∈ [0,1] , 1 ≤ < ∞, the rational Müntz operators are defined by (9). If Δ ≥ , = 1, 2, 3, .…”

An interpolation theorem and its applications to positive operators

“…It has been an open problem for some years to characterize those functions / for which \\K n f-f\\ L P = O{n~a) (0 < a < 1) (see [2,3,4,5,7]). We solved this characterization problem in [18,19] and now we give a somewhat different characterization by the aid of Theorem 1.…”