Optimal Linear Approximation Under General Statistical Convergence

Daniel Cárdenas-Morales () and Pedro Garrancho ()
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Daniel Cárdenas-Morales: University of Jaén, Department of Mathematics
Pedro Garrancho: University of Jaén, Department of Mathematics

A chapter in Advances in Summability and Approximation Theory, 2018, pp 191-202 from Springer

Abstract: Abstract This work deals with optimal approximation by sequences of linear operators. Optimality is meant here as asymptotic formulae and saturation results, a natural step beyond the establishment of both qualitative and quantitative results. The ordinary convergence is replaced by B -statistical $$\mathscr {A}$$ -summability, where B is a regular infinite matrix with non-negative real entries and $$\mathscr {A}$$ is a sequence of matrices of the aforesaid type, in such a way that the new notion covers the famous concept of almost convergence introduced by Lorentz, as well as a new one that merits being called statistical almost convergence.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-3077-3_12

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DOI: 10.1007/978-981-13-3077-3_12

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