Function-valued Korovkin systems without quasiconcavity and set-valued Korovkin systems without convexity Original Research Article

In this paper, we show how to construct Korovkin systems in spaces of continuous mappings whose values are (possibly non-convex) sets or more generally (possibly non-quasiconcave) upper semicontinuous functions. The Korovkin system is constructed from a given Korovkin system of real functions. Furthermore, we show that any Korovkin system in the quasiconcave case, augmented by all constant functions, is a Korovkin system for the general case.