Quantitative Korovkin theorems for monotone sublinear and strongly translatable operators in Lp([0,1]), 1 < P < ∞

被引：0

作者：

Gal, Sorin g. ^{[1
,2
]}

Niculescu, Constantin p. ^{[2
,3
]}

机构：

[1] Univ Oradea, Dept Math & Comp Sci, Oradea 410087, Romania

[2] Acad Romanian Scientists, Bucharest 050044, Romania

[3] Univ Craiova, Dept Math, Craiova 410087, Romania

来源：

ANNALES POLONICI MATHEMATICI | 2024年 / 132卷 / 02期

关键词：

Korovkin type theorems; monotone operator; sublinear operator; weakly nonlinear operator; C([0; 1])-space; Lp([0; 1 < p < oo; second order mod- ulus of smoothness; Lp-modulus of smoothness of orders 1 and 2; quantitative estimates; APPROXIMATION; CONVERGENCE;

D O I：

10.4064/ap230511-18-12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By extending the classical quantitative approximation results for positive linear operators in Lp([0, 1]), 1 <= p <= infinity, 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.

引用

页码：137 / 151

页数：16

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Quantitative Korovkin theorems for monotone sublinear and strongly translatable operators in Lp([0,1]), 1 &lt; P &lt; ∞

Quantitative Korovkin theorems for monotone sublinear and strongly translatable operators in Lp([0,1]), 1 < P < ∞