Approximation with Riemann-Liouville fractional derivatives

被引：0

作者：

Anastassiou, George A. ^{[1
]}

机构：

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

来源：

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA | 2019年 / 64卷 / 03期

关键词：

Riemann-Liouville fractional derivative; positive sublinear operators; modulus of continuity; comonotonic operator; Choquet integral;

D O I：

10.24193/subbmath.2019.3.07

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we study quantitatively with rates the pointwise convergence of a sequence of positive sublinear operators to the unit operator over continuous functions. This takes place under low order smothness, less than one, of the approximated function and it is expressed via the left and right Riemann-Liouville fractional derivatives of it. The derived related inequalities in their right hand sides contain the moduli of continuity of these fractional derivatives and they are of Shisha-Mond type. We give applications to Bernstein Max-product operators and to positive sublinear comonotonic operators connecting them to Choquet integral.

引用

页码：357 / 365

页数：9

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