Quantitative Korovkin theorems for monotone sublinear and strongly translatable operators in $L_{p}([0, 1])$, $1\le p\le \infty $
Volume 132 / 2024
Annales Polonici Mathematici 132 (2024), 137-151
MSC: Primary 41A35; Secondary 41A36, 41A63
DOI: 10.4064/ap230511-18-12
Published online: 4 March 2024
Abstract
By extending the classical quantitative approximation results for positive linear operators in $L_{p}([0, 1])$, $1\le p \le \infty $, of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of monotone sublinear and strongly translatable operators, we obtain quantitative estimates in terms of the second order and third order moduli of smoothness, in Korovkin type theorems. Applications to concrete examples are included and an open question concerning interpolation theory for sublinear, monotone and strongly translatable operators is raised.
