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
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Proje Numarası | Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni |
Yayımlanma Tarihi | 1 Eylül 2019 |
Yayımlandığı Sayı | Yıl 2019 |