The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called approximation process. First, we give a sufficient condition for this sequence to approximate the class of bounded, uniformly continuous functions. Then we present som...

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L-functions, by means of positive linear operators. The paper also contains several new results and applications. Moreover, the organization of the subject follows a simple and direct approach which quick...

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy ran...

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...