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On a conjecture concerning the sum of the squared Bernstein polynomials. (English) Zbl 1334.41005

Summary: We obtain a new representation of the sum of the squared Bernstein polynomials and use it to validate a conjecture asserting that this sum is a convex function. The result is extended to some other classical approximation operators.

MSC:

41A10 Approximation by polynomials
41A36 Approximation by positive operators
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