WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
On Kantorovich-type Operators in Lp Spaces
Author:
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 $$Lp([0,1]), p \geq 1 $$, spaces. By using the r-th order $$(r = 1 $$ and $$ r \geq 3) $$ 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 α-Hölder $$(0 < α \leq 1) $$ functions and the local approximation property.