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Approximation of Some Classes of Functions by Landau Type Operators

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Abstract

This paper aims to highlight a class of integral linear and positive operators of Landau type which have affine functions as fixed points. We focus to reveal approximation properties both in \(L_p\) spaces and in weighted \(L_p\) spaces \((1\le p<\infty )\). Also, we give an extension of the operators to approximate real-valued vector functions. In this case, the study pursues the approximation of continuous functions on convex compacts. The evaluation of the rate of convergence in one and multidimensional cases is performed by using adequate moduli of smoothness.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Str. Kogălniceanu, 1, 400084, Cluj-Napoca, Romania

    Octavian Agratini

  2. Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Str. Fântânele, 57, 400320, Cluj-Napoca, Romania

    Octavian Agratini

  3. Department of Mathematics, Kirikkale University, 71450, Yahşihan, Kirikkale, Turkey

    Ali Aral

Authors
  1. Octavian Agratini
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  2. Ali Aral
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Correspondence to Octavian Agratini.

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Dedicated to Professor Francesco Altomare on the occasion of his 70th birthday, with high esteem and friendship.

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Agratini, O., Aral, A. Approximation of Some Classes of Functions by Landau Type Operators. Results Math 76, 12 (2021). https://doi.org/10.1007/s00025-020-01319-9

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