Approximation of Bounded Continuous Functions by Linear Combinations of Phillips Operators

Demonstratio Mathematica

Tachev Gancho¹ 

[1] UNIVERSITY OF ARCHITECTURE DEPT. OF MATHEMATICS 1 Hristo Smirnenski, Blvd., 1046-SOFIA, BULGARIA;

关键词: and phrases: linear combinations;    Phillips operators;    simultaneous approximation;    Ditzian-Totik moduli of smoothness;   

DOI  :  10.2478/dema-2014-0053

来源: DOAJ

【 摘 要 】

We study the approximation properties of linear combinations of the so-called Phillips operators, which can be considered as genuine Szász-Mirakjan-Durrmeyer operators. As main result, we prove a direct estimate for the rate of approximation of bounded continuous functions f E C[0,x), measured in C|\[0,x)-norm and thus generalizing the results, proved earlier by Gupta, Agrawal, and Gairola in [3]. Our estimates rely on the recent results, obtained in the joint works of M. Heilmann and the author-[10, 11]

【 授权许可】

Unknown