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Strong Converse Inequality for Left Gamma Quasi-Interpolants

Authors:	Qiu-lan Qi Shun-sheng Guo

Institution:	(1) College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China

Abstract:	Abstract The rate of convergence for the Gamma operators cannot be faster than $O{\left( {\frac{1} {n}} \right)}$ . In order to obtain much faster convergence, quasi-interpolants in the sense of Sablonnière are considered. For the first time in the theory of quasi-interpolants, the strong converse inequality is solved in sup-norm with the K-functional $K^{\alpha }_{\lambda } {\left( {f,t^{{2r}} } \right)}{\left( {0 \leqslant \lambda \leqslant 1,0 < \alpha < 2r} \right)}$ . Supported by the Hebei Provincial Science Foundation of China (A2004000137); Doctoral Research Fund of Hebei Normal University (L2002B03)

Keywords:	gamma quasi-interpolant strong converse inequality K-functional
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