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The product of two functions using positive linear operators. (English) Zbl 1463.41053

Summary: In this paper we estimate the speed of convergence of the difference \(L_n(fg)-(L_n f)\cdot (L_n g)\) towards \(0\), where \((L_n)\) are positive linear operators used in the approximation of continuous functions. We also study in what conditions the formula \({L'_n}(fg)-f {L'_n}g-g {L'_n}f \to 0\) holds true.

MSC:

41A36 Approximation by positive operators
41A25 Rate of convergence, degree of approximation
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