Korovkin theorems on weighted spaces: revisited
The paper contains new, direct and easy proofs of the Korovkin theorems for positive linear operators acting on weighted spaces. An important tool is a lemma of \textit{A. D. Gadziev} [Mat. Zametki 20, 781--786 (1976; Zbl 0383.41016)]. Using it, the authors revise the proofs of some of their earlier results. First, the ordinary approximation process by positive linear operators acting between weighted spaces is investigated and quantitative results are obtained. Then applications and examples are given, using different notions of convergence, such as statistical convergence, summation processes, Abel's method.
scientific article; zbMATH DE number 6851243
scientific article