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A Review of the Chebyshev Inequality Pertaining to Fractional Integrals

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  • Péter Kórus

    (Department of Mathematics, Juhász Gyula Faculty of Education, University of Szeged, Hattyas utca 10, H-6725 Szeged, Hungary
    These authors contributed equally to this work.)

  • Juan Eduardo Nápoles Valdés

    (Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Ave. Libertad 5450, Corrientes 3400, Argentina
    Facultad Regional Resistencia, Universidad Tecnológica Nacional, French 414, Resistencia, Chaco 3500, Argentina
    These authors contributed equally to this work.)

Abstract

In this article, we give a brief review of a well-known integral inequality that gives information about the integral of the product of two functions using synchronous functions, the Chebyshev inequality. We have compiled the most relevant information about fractional and generalized integrals, which are one of the most dynamic topics in today’s mathematical sciences. After presenting the classical formulation of the inequality using Lebesgue integrable functions, the most general results known from the literature are collected in an attempt to present the reader with a current overview of this research topic.

Suggested Citation

  • Péter Kórus & Juan Eduardo Nápoles Valdés, 2025. "A Review of the Chebyshev Inequality Pertaining to Fractional Integrals," Mathematics, MDPI, vol. 13(7), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1137-:d:1624212
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    References listed on IDEAS

    as
    1. Set, Erhan & Akdemi̇r, Ahmet Ocak & Karaoğlan, Ali̇, 2024. "New integral inequalities for synchronous functions via Atangana–Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    2. Haruhiko Ogasawara, 2020. "The multivariate Markov and multiple Chebyshev inequalities," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(2), pages 441-453, January.
    3. Set, Erhan & Kashuri, Artion & Mumcu, İlker, 2021. "Chebyshev type inequalities by using generalized proportional Hadamard fractional integrals via Polya–Szegö inequality with applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. 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.
    5. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad & Muhammad Samraiz & Tepper L Gill, 2020. "Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function," Journal of Mathematics, Hindawi, vol. 2020, pages 1-14, November.
    6. D. Baleanu & S. D. Purohit, 2014. "Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    7. D. Baleanu & S. D. Purohit, 2014. "Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    9. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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