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Optimal Linear Approximation Under General Statistical Convergence

In: Advances in Summability and Approximation Theory

Author

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  • Daniel Cárdenas-Morales

    (University of Jaén, Department of Mathematics)

  • Pedro Garrancho

    (University of Jaén, Department of Mathematics)

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.

Suggested Citation

  • Daniel Cárdenas-Morales & Pedro Garrancho, 2018. "Optimal Linear Approximation Under General Statistical Convergence," Springer Books, in: S. A. Mohiuddine & Tuncer Acar (ed.), Advances in Summability and Approximation Theory, pages 191-202, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-3077-3_12
    DOI: 10.1007/978-981-13-3077-3_12
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