A Korovkin-type theorem in the space of Riemann integrable functions
We give a characterization of the Korovkin subspaces of the space \({\mathcal R}(X)\) of Riemann integrable functions over a Hausdorff compact topological space X, equipped with the \({\mathcal R}\)-sequential convergence. Some applications are presented in the context of the space of \(2\pi\)- periodic real functions which are Riemann integrable on the compact real interval [0,2\(\pi\) ] and of the space of Riemann integrable functions on the standard simplex and the hypercube of \({\mathbb{R}}^ p\) (p\(\geq 1)\).
Korovkin subspaces of the space of Riemann integrable functions over a Hausdorff compact topological space
scientific article; zbMATH DE number 4090170