On quantitative approximation (Q1343404)

This note is concerned with quantitative approximation by positive linear operators defined on \(C_ R(X, d)\). Here \((X, d)\) is a compact metric space with diameter \(d(X)\) satisfying \(0< d(X)< \infty\) and \(C_ R(X, d)\) is the Banach lattice of continuous real functions on \(X\) endowed with the supremum norm. The first result of this type for \(X\) a compact interval under the usual distance function was given by \textit{R. G. Mamedov} [Dokl. Akad. Nauk SSSR 128, 674-676 (1959; Zbl 0089.114)].