Abstract
This note is devoted to the study of a linear positive sequence of operators representing an integral form in Kantorovich’s sense. We prove that this sequence converges to the identity operator in \(Lp([0,1]),\) \(p\geq1,\) spaces. By using the \(r\)-th order \((r=1\) and \(r\geq3)\) modulus of smoothness measured in these spaces, we establish an upper bound of the approximation error. Also, we point out a connection between the smoothness of \(\alpha\)-H\”{o}lder \((0<\alpha \leq1)\) functions and the local approximation property.
Authors
Octavian Agratini
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Keywords
Positive linear operator; Kantorovich-type operator; Lp space, rate of convergence; Bohman-Korovkin theorem; r-modulus of smoothness; K-functional; Hardy-Littlewood maximal operator.
Paper coordinates
O. Agratini, On Kantorovich-type operators in Lp spaces, WSEAS Transactions on Mathematics, 23 (2024), pp. 1033-1038, https://doi.org/10.37394/23206.2024.23.106
About this paper
Journal
Wseas Transactions on Mathematics
Publisher Name
WSEAS
Print ISSN
1109-2769
Online ISSN
2224-2880
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