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Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces

Author

Listed:
  • Saad Ihsan Butt

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Punjab 54000, Pakistan)

  • Josip Pečarić

    (Croatian Academy of Sciences and Arts, 10000 Zagreb, Croatia)

  • Sanja Tipurić-Spužević

    (Faculty of Chemistry and Technology, University of Split, Rudera Boškovića 35, 21000 Split, Croatia)

Abstract

The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, and extensions. In the present article, we provide generalizations of Sokolov’s inequality in weighted Lebesgue L ω Ω , A , μ spaces by employing the weighted Sonin’s identity and Čebyšev functional. As a result, we provide a generalized Grüss inequality in which the bounding constants are improved with bounding functions in L ω p Ω , A , μ spaces. As an application, we provide several new bounds for Jensen–Grüss type differences.

Suggested Citation

  • Saad Ihsan Butt & Josip Pečarić & Sanja Tipurić-Spužević, 2023. "Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces," Mathematics, MDPI, vol. 11(7), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1756-:d:1117639
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    References listed on IDEAS

    as
    1. Ahmet Ocak Akdemir & Saad Ihsan Butt & Muhammad Nadeem & Maria Alessandra Ragusa, 2021. "New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    2. Aglić Aljinović, A. & Pečarić, J. & Tipurić-Spužević, S., 2015. "Weighted quadrature rules via Grüss type inequalities for weighted Lp spaces," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 1-12.
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