On the rate of convergence of some discrete operators

Grazyna Aniol
1994 Demonstratio Mathematica  
We consider a certain class of discrete approximation operators L n which include e.g. the Bernstein polynomials, the Baskakov operators, the Meyer-Konig and Zeller operators or the Favard operators. For bounded or some locally bounded functions / on an interval I there is estimated the rate of convergence of i n [/](x) at these points x at which the one-sided limits /(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used. (3) 6n(x) := 53 Pj, n (x) -1 -> 0 as n -• oo j€Jn Research supported by KBN grant 2 1079 91 01
doi:10.1515/dema-1994-0213 fatcat:rmaoa543ebevzgwzv26jkrw52e