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Direct Estimates of the Rate of Approximation by the Kantorovich Operator in Variable Exponent Lebesgue Spaces

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Abstract

We establish two direct estimates by K-functionals of the rate of approximation by the Kantorovich operators in variable exponent Lebesgue spaces. They extend known results in the non-variable exponent Lebesgue spaces. The approach applied heavily relies on the boundedness of the Hardy–Littlewood maximal operator.

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Funding

This study is financed by the European Union-NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, Project No. BG-RRP-2.004-0008.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 5 James Bourchier Blvd., 1164, Sofia, Bulgaria

    Borislav R. Draganov & Ivan Gadjev

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, bl. 8 Acad. G. Bonchev Str., 1113, Sofia, Bulgaria

    Borislav R. Draganov

Authors
  1. Borislav R. Draganov
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  2. Ivan Gadjev
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B. R. Draganov and I. Gadjev have contributed equally to this work.

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Correspondence to Borislav R. Draganov.

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This study is financed by the European Union-NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, Project No. BG-RRP-2.004-0008.

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Draganov, B.R., Gadjev, I. Direct Estimates of the Rate of Approximation by the Kantorovich Operator in Variable Exponent Lebesgue Spaces. Mediterr. J. Math. 21, 112 (2024). https://doi.org/10.1007/s00009-024-02650-z

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  • DOI: https://doi.org/10.1007/s00009-024-02650-z

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