A Sequence of Kantorovich-Type Operators on Mobile Intervals

In this paper, we introduce and study a new sequence of positive linear operators, acting on both spaces of continuous functions as well as spaces of integrable functions on [0,1]. We state some qualitative properties of this sequence and we prove that it is an approximation process both in C([0,1]) and in L^p([0,1]), also providing some estimates of the rate of convergence. Moreover, we determine an asymptotic formula and, as an application, we prove that certain iterates of the operators converge, both in C([0,1]) and, in some cases, in L^p([0,1]), to a limit semigroup. Finally, we show that our operators, under suitable hypotheses, perform better than other existing ones in the literature.