Strong Converse Inequality for Left Gamma Quasi-Interpolants

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 Sablonniere 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 $$ K^{\alpha }_{\lambda } {\left( {f,t^{{2r}} } \right)}\;{\left( {0 \leqslant \lambda \leqslant 1,\;0 < \alpha < 2r} \right)} $$ .