Global smoothness and uniform convergence of smooth Poisson-Cauchy type singular operators

被引:4
|
作者
Anastassiou, George A. [1 ]
Mezei, Razvan A. [1 ]
机构
[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
关键词
Simultaneous global smoothness; Simultaneous approximation; Poisson-Cauchy type singular integral; Modulus of smoothness; Rate of convergence; INTEGRALS;
D O I
10.1016/j.amc.2009.07.030
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article we introduce the smooth Poisson-Cauchy type singular integral operators over the real line. Here we study their simultaneous global smoothness preservation property with respect to the L-p norm, 1 <= p <= infinity, by involving higher order moduli of smoothness. Also we study their simultaneous approximation to the unit operator with rates involving the modulus of continuity with respect to the uniform norm. The produced Jackson type inequalities are almost sharp containing elegant constants, and they reflect the high order of differentiability of the engaged function. (C) 2009 Elsevier Inc. All rights reserved.
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页码:1718 / 1731
页数:14
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