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Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application

Author

Listed:
  • Sanja Kovač

    (Faculty of Geotechnical Engineering, University of Zagreb, 42000 Varaždin, Croatia)

  • Ana Vukelić

    (Faculty of Food and Biotechnology, University of Zagreb, 10000 Zagreb, Croatia)

Abstract

Recently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to L p spaces. In the existing literature, the main assumption in the weight-type results is that the derivative of the function is bounded by two constant functions. The aim of our paper is to extend those results in a way that the derivative of the function is bounded by two functions in L p spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas.

Suggested Citation

  • Sanja Kovač & Ana Vukelić, 2022. "Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application," Mathematics, MDPI, vol. 10(5), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:735-:d:758905
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    Citations

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    Cited by:

    1. Mohammad W. Alomari & Christophe Chesneau & Víctor Leiva, 2022. "Grüss-Type Inequalities for Vector-Valued Functions," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    2. Mohammad W. Alomari & Christophe Chesneau & Víctor Leiva & Carlos Martin-Barreiro, 2022. "Improvement of Some Hayashi–Ostrowski Type Inequalities with Applications in a Probability Setting," Mathematics, MDPI, vol. 10(13), pages 1-15, July.

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