Optimal Simultaneous Approximation via 𝒜-Summability - Francisco Aguilera; Daniel Cárdenas-Morales; Pedro Garrancho (Abstract and Applied Analysis)
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.