On Szász–Mirakyan Operators Preserving \(\varvec{e^{2ax}},\)
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- 作者：Tuncer Acar ; Ali Aral ; Heiner Gonska
- 关键词：Szász–Mirakyan operators ; King operators ; Weighted modulus of continuity ; Uniform convergence
- 刊名：Mediterranean Journal of Mathematics
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：14
- 期：1
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Springer International Publishing
- ISSN：1660-5454
- 卷排序：14
文摘
A modification of Szász–Mirakyan operators is presented that reproduces the functions 1 and \(e^{2ax}\), \(a>0\) fixed. We prove uniform convergence, order of approximation via a certain weighted modulus of continuity, and a quantitative Voronovskaya-type theorem. A comparison with the classical Szász–Mirakyan operators is given. Some shape preservation properties of the new operators are discussed as well. Using a natural transformation, we also present a uniform error estimate for the operators in terms of the first- and second-order moduli of smoothness.