Advances in Summability and Approximation Theory pp 191-202 | Cite as

# Optimal Linear Approximation Under General Statistical Convergence

## 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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