Convergence Properties of Certain Positive Linear Operators

被引：1
|
作者：
Acu, Ana-Maria [1 ]
Manav, Nesibe [2 ]
Ratiu, Augusta [1 ]
机构：
[1] Lucian Blaga Univ Sibiu, Dept Math & Informat, Str Dr I Ratiu 5-7, Sibiu 550012, Romania
[2] Gazi Univ, Sci Fac, Dept Math, TR-06500 Ankara, Turkey
来源：
RESULTS IN MATHEMATICS | 2019年 / 74卷 / 01期
关键词：
Voronovskaja type theorem; Ditzian-Totik modulus of smoothness; linear positive operators; APPROXIMATION PROPERTIES; DURRMEYER; VARIANT;
D O I：
10.1007/s00025-018-0931-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The present paper deals with the modified positive linear operators that present a better degree of approximation than the original ones. This new construction of operators depend on a certain function defined on [0, 1]. Some approximation properties of these operators are given. Using the first order Ditzian-Totik modulus of smoothness, some Voronovskaja type theorems in quantitative mean are proved. The main results proved in this paper are applied for Bernstein operators, Lupas operators and genuine Bernstein-Durrmeyer operators. By numerical examples we show that depending on the choice of the function , the modified operator presents a better order of approximation than the classical ones.
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页数：24
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