Iterates of Bernstein type operators on a square with one curved side via contraction principle. (English) Zbl 1285.41013

The paper under review is especially a continuation of one by P. Blaga et al. [Stud. Univ. Babeş-Bolyai, Math. 55, No. 3, 51–68 (2010; Zbl 1224.41001)]. The authors consider some Bernstein-type operators as well as their iterates, their product and Boolean sum operators defined on a square with one curved side. For functions defined on a square with one curved side, they obtain convergence results using the techniques of the weakly Picard operators and the contraction principle.


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


Zbl 1224.41001
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