Optimal Simultaneous Approximation via 𝒜 -Summability

Abstract

We present optimal convergence results for the mth derivative of a function by sequences of linear operators. The usual convergence is replaced by $𝒜$-summability, with $𝒜$ 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.