Pointwise Approximation by Sz\`{a}sz-Mirakjan Quasi-Interpolants

Abstract:

      Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Sz\`{a}sz-Mirakjan Quasi--Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus $\omega^{2r}_{\varphi}(f,t)$. In this paper, we extend Diallo's result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions $f\in C_B[0,\infty)$ by making use of the unified modulus $\omega^{2r}_{\varphi^{\lambda}}(f,t)$ $(0\le \lambda\le 1)$.