Some Aspects of Korovkin-Type Theorem and Positive Operators

Abstract

This thesis is concerned with Korovkin-type approximation theory and its applications using positive linear operators. In particular, if (Tn) is a sequence of positive linear operators on C([0,1]) such that Tn(f ) con verges uniformly to f for f ∈ {1,x,x 2 }, then this is sufficient to ensure the uniform convergence of Tn(f ) for all f ∈ C([0,1]). Moreover, the work investigates some convergence criteria for nets (or generalized se quences) of positive operators on function spaces. It also presents several new results and applications that allow readers to quickly grasp the main classical results of the theory as well as some recent developments.