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𝒜 $$\mathcal{A}$$ -Summability of Sequences of Linear Conservative Operators

In: Mathematical Analysis, Approximation Theory and Their Applications

Author

Listed:
  • Daniel Cárdenas-Morales

    (University of Jaén)

  • Pedro Garrancho

    (University of Jaén)

Abstract

This work deals with the approximation of functions by sequences of linear operators. Here the classical convergence is replaced by matrix summability. Beyond the usual positivity of the operators involved in the approximation processes, more general conservative approximation properties are considered. Quantitative results, as well as results on asymptotic formulae and saturation are stated. It is the intention of the authors to show the way in which some concepts of generalized convergence entered Korovkin-type approximation theory. This is a survey work that gathers and orders the results stated by the authors and other researchers within the aforesaid subject.

Suggested Citation

  • Daniel Cárdenas-Morales & Pedro Garrancho, 2016. "𝒜 $$\mathcal{A}$$ -Summability of Sequences of Linear Conservative Operators," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 463-482, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31281-1_20
    DOI: 10.1007/978-3-319-31281-1_20
    as

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