Approximation theorems for certain positive linear operators

被引:3
作者
Mahmudov, N. I. [1 ]
机构
[1] Eastern Mediterranean Univ, TRNC, TR-10 Gazimagusa, Mersin, Turkey
关键词
Korovkin approximation; Positive operator; q-Lupas-Bernstein; omega; q-Bernstein operator; Iterates; Q-BERNSTEIN POLYNOMIALS;
D O I
10.1016/j.aml.2010.03.016
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work we prove approximation theorems for certain positive linear operators via Ditzian-Totik moduli omega(2,phi) (f, .) of second order where the step-weights are functions whose squares are concave. The results obtained are applied to the q-Lupas-Bernstein operators, the omega, q-Bernstein operators and the convergence of the iterates of the q-Bernstein polynomials. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码:812 / 817
页数:6
相关论文
共 10 条
[1]  
Ditzian Z., 1987, Springer Series in Computational Mathematics
[2]   Local and global approximation theorems for positive linear operators [J].
Felten, M .
JOURNAL OF APPROXIMATION THEORY, 1998, 94 (03) :396-419
[3]   Generalized Bernstein polynomials [J].
Lewanowicz, S ;
Wozny, P .
BIT NUMERICAL MATHEMATICS, 2004, 44 (01) :63-78
[4]  
LUPAS A, 1987, SEM NUM STAT CALC 9
[5]   Korovkin-type theorems and applications [J].
Mahmudov, Nazim I. .
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2009, 7 (02) :348-356
[6]   q-Bernstein polynomials and their iterates [J].
Ostrovska, S .
JOURNAL OF APPROXIMATION THEORY, 2003, 123 (02) :232-255
[7]  
Ostrovska S, 2007, J Math Anal Approx Theory, V2, P35
[8]   A survey of results on the q-Bernstein polynomials [J].
Phillips, George M. .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2010, 30 (01) :277-288
[9]   Properties of convergence for ω, q-Bernstein polynomials [J].
Wang, Heping .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 340 (02) :1096-1108
[10]   Korovkin-type theorem and application [J].
Wang, HP .
JOURNAL OF APPROXIMATION THEORY, 2005, 132 (02) :258-264