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Optimal Linear Approximation Under General Statistical Convergence

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Advances in Summability and Approximation Theory

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.

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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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Authors and Affiliations

  1. Department of Mathematics, University of Jaén, Campus Las Lagunillas s/n, 23071, Jaén, Spain

    Daniel Cárdenas-Morales & Pedro Garrancho

Authors
  1. Daniel Cárdenas-Morales
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  2. Pedro Garrancho
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Correspondence to Daniel Cárdenas-Morales .

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Editors and Affiliations

  1. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    S. A. Mohiuddine

  2. Department of Mathematics, Selçuk University, Selçuklu, Konya, Turkey

    Tuncer Acar

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Cárdenas-Morales, D., Garrancho, P. (2018). Optimal Linear Approximation Under General Statistical Convergence. In: Mohiuddine, S., Acar, T. (eds) Advances in Summability and Approximation Theory. Springer, Singapore. https://doi.org/10.1007/978-981-13-3077-3_12

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