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Inverse Estimates and Saturation Results for Linear Combinations

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Approximation with Positive Linear Operators and Linear Combinations

Part of the book series: Developments in Mathematics ((DEVM,volume 50))

Abstract

Let the Ditzian–Totik moduli of smoothness ω φ r(f, t) p be given as (2.1.2) and the equivalent K-functional K r, φ (f, t r) p be given as (2.1.4). As in Section 2.1, we suppose the same definitions for the weight function φ(x) and for the domain D of the operators \(B_{n},S_{n},V _{n},\widehat{B}_{n},\widehat{S}_{n},\widehat{V }_{n}.\) To establish the inverse results for approximation by L n, r we need two Bernstein type inequalities and the Berens–Lorentz lemma , which results we formulate as follows:

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Authors and Affiliations

  1. Department of Mathematics, Netaji Subhas Institute of Technology, New Delhi, India

    Vijay Gupta

  2. Department of Mathematics, University of Architecture Civil Engineering and Geodesy, Sofia, Bulgaria

    Gancho Tachev

Authors
  1. Vijay Gupta
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  2. Gancho Tachev
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Gupta, V., Tachev, G. (2017). Inverse Estimates and Saturation Results for Linear Combinations. In: Approximation with Positive Linear Operators and Linear Combinations. Developments in Mathematics, vol 50. Springer, Cham. https://doi.org/10.1007/978-3-319-58795-0_3

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