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Optimal Linear Approximation Under General Statistical Convergence

  • Daniel Cárdenas-MoralesEmail author
  • Pedro Garrancho
Chapter

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.

Notes

Acknowledgements

This work is partially supported by Junta de Andalucía, Spain (Research group FQM-0178). The first author is also partially supported by Research Projects DGA (E-64), MTM2015-67006-P and by FEDER funds.

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of JaénJaénSpain

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