A nonlinear version of Kantorovich operators with p-averages: convergence results and asymptotic formula

In this paper, we modify the classical Kantorovich operators, very well known inApproximation Theory, by considering p-averages (whose expressions are of the form of Lp (quasi-)norms, p > 0). We establish convergence results, an asymptotic formulacovering the general setting; moreover, we show that, under suitable assumptions, ouroperators perform better than the classical Kantorovich ones in approximating functions. Because of the nature of the p-averages, the proposed operators are nonlinear, so their study turns out to be more challenging.