Iterates of multivariate Cheney-Sharma operators. (English) Zbl 1275.41029

Summary: Using the weakly Picard operators technique, we study the convergence of the iterates of some bivariate and trivariate Cheney-Sharma operators. Also, we generalize the procedure for the multivariate case.


41A36 Approximation by positive operators
41A05 Interpolation in approximation theory
41A25 Rate of convergence, degree of approximation
39B12 Iteration theory, iterative and composite equations
47H10 Fixed-point theorems