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On a New Modification of Baskakov Operators with Higher Order of Approximation

Author

Listed:
  • Ivan Gadjev

    (Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Parvan Parvanov

    (Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Rumen Uluchev

    (Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
    These authors contributed equally to this work.)

Abstract

A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on [ 0 , ∞ ) . We study the approximation error of the proposed operator. Our main results are a direct theorem and strong converse theorem with respect to a related K-functional. Both theorems give complete characterization of the uniform approximation error in means of the K-functional. The new operator suggested by the authors is linear but non-positive. However, it has the advantage of a higher order of approximation compared to the Goodman–Sharma variant of the Baskakov operator defined in 2005 by Finta. The results of computational simulations are given.

Suggested Citation

  • Ivan Gadjev & Parvan Parvanov & Rumen Uluchev, 2024. "On a New Modification of Baskakov Operators with Higher Order of Approximation," Mathematics, MDPI, vol. 13(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:64-:d:1554877
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