A Korovkin theorem in multivariate modular function spaces. (Q841311)

The classical Korovkin theorem states that uniform convergence in \(C([a,b])\) (the space of the continuous real functions defined on an interval of the real axis) of a sequence of positive linear operators holds if and only if uniform convergence holds for the three test functions \(\{1,x,x^2\}\). In the present paper a modular version of this result is given for multivariate modular function spaces. Applications to some multivariate discrete and integral operators, acting in Orlicz spaces, are given.