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.
Kantorovich-type operators Positive approximation processes Rate of convergence Asymptotic formula Generalized convexity
INdAM - GNAMPA
Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni
Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Articles |
Authors | |
Project Number | Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni |
Publication Date | September 1, 2019 |
Published in Issue | Year 2019 |