TY - JOUR
AU - Gonska, Heiner
PY - 2023/12/28
Y2 - 2024/11/10
TI - The rate of convergence of bounded linear processes on spaces of continuous functions
JF - J. Numer. Anal. Approx. Theory
JA - J. Numer. Anal. Approx. Theory
VL - 52
IS - 2
SE - Articles
DO - 10.33993/jnaat522-1326
UR - https://ictp.acad.ro/jnaat/journal/article/view/1326
SP - 182-232
AB - <p>Quantitative Korovkin-type theorems for approximation by bounded linear operators defined on \(C(X,d)\) are given, where \((X,d)\) is a compact metric space. Special emphasis is on positive linear operators.<br />As is known from previous work of Newman and Shapiro, Jimenez Pozo, Nishishiraho and the author, among others, there are two possible ways to obtain error estimates for bounded linear operator approximation: the so-called direct approach, and the smoothing technique.<br />We give various generalizations and refinements of earlier results which were obtained by using both techniques. Furthermore, it will be shown that, in a certain sense, none of the two methods is superior to the other one.</p>
ER -