A Review of the Chebyshev Inequality Pertaining to Fractional Integrals

Péter Kórus () and Juan Eduardo Nápoles Valdés
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Péter Kórus: Department of Mathematics, Juhász Gyula Faculty of Education, University of Szeged, Hattyas utca 10, H-6725 Szeged, Hungary
Juan Eduardo Nápoles Valdés: Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Ave. Libertad 5450, Corrientes 3400, Argentina

Mathematics, 2025, vol. 13, issue 7, 1-12

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.

Keywords: Chebyshev’s inequality; synchronous functions; fractional calculus; fractional integral operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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