Approximation results for a general class of Kantorovich type operators

We introduce and study a family of integral operators in the Kantorovich sense for functions acting on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform convergence and in the setting of Orlicz spaces with respect to the modular convergence. Moreover, we show how our theory applies to several classes of integral and discrete operators, as the sampling, convolution and Mellin type operators in the Kantorovich sense, thus obtaining a simultaneous approach for discrete and integral operators. Further, we derive our general convergence results for particular cases of Orlicz spaces, as $L^p-$spaces, interpolation spaces and exponential spaces. Finally we construct some concrete example of our operators and we show some graphical representations.