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Bernstein-type operators on a triangle with one curved side. (English) Zbl 1258.41009

The authors construct Bernstein-type operators, and their product and Boolean sum, for a triangle with one curved side. Their interpolation properties and the order of accuracy are studied. Moreover, using the modulus of continuity and Peano’s theorem, respectively, the remainders of the corresponding approximation formulas are also studied. Finally, some numerical examples are given.

MSC:

41A36 Approximation by positive operators
41A35 Approximation by operators (in particular, by integral operators)
41A25 Rate of convergence, degree of approximation
41A80 Remainders in approximation formulas
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