We introduce the Aldaz-Kounchev-Render operators on a multidimensional simplex. In the case of the unit simplex of Rm these operators preserve the functions 1,x1j,…,xmj, j a positive integer. The Voronovskaja formula, the behaviour with respect to the convex function, and the limit of iterates of the operators are investigated.
Aldaz-Kounchev-Render operators on simplices
De Marchi S.;
2024
Abstract
We introduce the Aldaz-Kounchev-Render operators on a multidimensional simplex. In the case of the unit simplex of Rm these operators preserve the functions 1,x1j,…,xmj, j a positive integer. The Voronovskaja formula, the behaviour with respect to the convex function, and the limit of iterates of the operators are investigated.
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