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Optimal simultaneous approximation via \(\mathcal{A}\)-summability. (English) Zbl 1470.41011

Summary: We present optimal convergence results for the \(m\)th derivative of a function by sequences of linear operators. The usual convergence is replaced by \(\mathcal{A}\)-summability, with \(\mathcal{A}\) being a sequence of infinite matrices with nonnegative real entries, and the operators are assumed to be \(m\)-convex. Saturation results for nonconvergent but almost convergent sequences of operators are stated as corollaries.

MSC:

41A35 Approximation by operators (in particular, by integral operators)
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