Generalization of the left Bernstein quasi-interpolants (Q1270282)

The so-called left Bernstein quasi-interpolants, introduced by \textit{P. Sablonnière} [in Multivariate Approximation Theory, Vol. IV, (ISNM 90, 287-294 (1989; Zbl 0688.41007)], have very good convergence and stability properties proved by \textit{P. Sablonnière} [Approximation Theory Appl. 8, No. 3, 62-76 (1992; Zbl 0772.41024)] and by \textit{Z.-C. Wu} [J. Approximation Theory 66, No. 1, 36-43 (1991; Zbl 0742.41029)]. In this paper the author gives a sufficient condition for general operators to have similar good properties to those of the Sablonnière operator. He derives more general and more detailed results which imply all the preceding ones.