A Sequence of Kantorovich-Type Operators on Mobile Intervals

Year 2019, Volume: 2 Issue: 3, 130 - 143, 01.09.2019

Mirella Cappellettı Montano Vita Leonessa

https://doi.org/10.33205/cma.571078

Cited By: 4

Abstract

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. 

Keywords

Kantorovich-type operators, Positive approximation processes, Rate of convergence, Asymptotic formula, Generalized convexity

Supporting Institution

INdAM - GNAMPA

Project Number

Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni

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