Rearrangement inequality

Integrable system

Pure mathematics

Mathematics

Biology

Fractional calculus

Mathematical analysis

Chebyshev filter

Ecology

Multidimensional Chebyshev's inequality

Type (biology)

Inequality

Log sum inequality

Chebyshev's inequality

Applied mathematics

Markov's inequality

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators