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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.

MSC:

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
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