Rate of convergence of positive linear operators using an extended complete Tchebycheff system
Abstract
Let [a,b] ⊂ Rand let {Lj}j ε{lunate} N be a sequence of positive linear operators from Cn + 1([a, b]) to C([a, b]), n ≥ 0. The convergence of Lj to the unit operator I is closely related to the weak convergence of a sequence of positive finite measures μj to the unit measure δt, t ε{lunate} [a, b]. Very general estimates with rates are given for the error |∝[a, b] f dμj - f(t)|, where f ε{lunate} Cn + 1([a, b]), in the presence of an extended complete Tchebycheff system. These lead to sharp or nearly sharp inequalities of Shisha-Mond type and are connected to the theory of best L1 approximations by generalized polynomials. © 1989.
Publication Title
Journal of Approximation Theory
Recommended Citation
Anastassiou, G. (1989). Rate of convergence of positive linear operators using an extended complete Tchebycheff system. Journal of Approximation Theory, 59 (2), 125-149. https://doi.org/10.1016/0021-9045(89)90149-4
