CONVERGENCE THEOREMS IN ORLICZ AND BOGEL CONTINUOUS FUNCTIONS SPACES BY MEANS OF KANTOROVICH DISCRETE TYPE SAMPLING OPERATORS

Abstract

In this study, we prove the convergence theorems on the space of compactly supported functions and in the general setting of Orlicz spaces for a general class of Kantorovich type discrete operators defined by Carlo Bardaro and Ilaria Mantellini. We also define the generalized Boolean sum (GBS) operator for the class of bivariate Kantorovich type discrete operators and examine the approximation properties of GBS operators in the space of Bogel functions.