Approximation Results for a General Class of Kantorovich Type Operators

AbstractWe introduce and study a family of integral operators in the Kantorovich sense acting onfunctions defined on locally compact topological groups. We obtain convergence resultsfor the above operators with respect to the pointwise and uniform convergence and in thesetting of Orlicz spaces with respect to the modular convergence. Moreover, we showhow our theory applies to several classes of integral and discrete operators, as sampling,convolution and Mellin type operators in the Kantorovich sense, thus obtaining a simulta-neous approach for discrete and integral operators. Further, we obtain general convergenceresults in particular cases of Orlicz spaces, as L p −spaces, interpolation spaces and expo-nential spaces. Finally we construct some concrete examples of our operators and we showsome graphical representations. 2000 Mathematics Subject Classification . 41A35, 46E30, 47A58, 47B38, 94A12, 94A20 . Keywords . Orlicz spaces, modular convergence, Kantorovich sampling type operators, Kantorovich convolution type operators, KantorovichMellin type operators, estimates, pointwise convergence, uniform convergence.