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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.

MSC:

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

Citations:

Zbl 1224.41001
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