  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.

Functional Analysis