ESTIMATES OF THE APPROXIMATION ERROR FOR ABSTRACT SAMPLING TYPE OPERATORS IN ORLICZ SPACES

We get some inequalities concerning the modular distance I phi(G)[T f- f]for bounded functions f: G R. Here G is a locally compact Hausdorff topological space provided with a regular and sigma-finite measure mu(G) ,I phi(G) is the modular functional generating the Orlic zspaces L phi(G) and T is a nonlinear integral operator of the form (Tf) (s) = integral (H) K (s; t; f (t))d mu H (t), where H is a closed subset of G endowed with another regular and sigma-finite measure mu(H).As a consequence we obtain a convergence theorem for a net of such operators.Some applications to discrete operators are given