| Strong Converse Inequality for Sz\'{a}sz Operators |
| Received:May 05, 2006 Revised:January 16, 2007 |
| Key Words:
strong converse inequality Sz\'{a}sz operators Ditzian modulous.
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| Fund Project:the National Natural Science Foundation of China (No. 10571040); the Natural Science Foundation of Hebei Province (No. A2004000137); the Doctorial Fund of Education Department of Hebei Province (No. B2004118); the Doctorial Fund of Hebei Normal University |
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| Abstract: |
| In this paper, we obtain the strong converse inequality for Sz\'{a}sz operators with $K$-functional by introducing a new $K$-functional of the form $$K_{\lambda}^{\alpha}(f,t^2)=\inf_{g\in C_{\lambda}^2}\{\|f-g\|_0+t^2\|g\|_2\}\; \;(0\leq \lambda\leq 1, 0<\alpha<2),$$ where $\|\cdot\|_{0}, \|\cdot\|_2, C_\lambda^2 $ are defined in the paper. As for its applications, we have extended some results before this paper. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.01.019 |
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