The rate of convergence for the Gamma operators cannot be faster than O( 1 n ). 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 α λ (f, t 2r ) (0 ≤ λ ≤ 1, 0 < α < 2r).