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

Cătinaş, Teodora; Otrocol, Diana

Fixed Point Theory 14, No. 1, 97-106 (2013).

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.

Reviewer: Harun Karsli (Bolu)

MSC:

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

Keywords:

weakly Picard operators; iterated Bernstein-type operators; square with curved side; contraction principle; convergence

Citations:

Zbl 1224.41001