Geodesic
Generalizations of some integral inequalities for Riemann--Liouville operator
Čebyševskij sbornik, Tome 23 (2022) no. 2, pp. 161-169

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The Chebyshev inquality is one of important inequalities in mathematics. It's a necessary tool in probability theory. The item of Chebyshev's inequality may also refer to Markov's inequality in the context of analysis. In[6, 7], using the usual Riemann–Liouville fractional integral operator $I^{\alpha }$, were established and proved some new integral inequalities for the Chebyshev fonctional \begin{equation} \nonumber T(f,g):=\frac{1}{b-a}\int^{b}_{a}f(x)g(x)dx-\frac{1}{b-a}\int^{b}_{a}f(x)dx\frac{1}{b-a}\int^{b}_{a}g(x)dx. \end{equation} In this work, we give some generalizations of Chebyshev-type integral inequalities by using Riemann—Liouville fractional integrals of function with respect to another function.
Keywords: Fractional integral, Chebyshev's inequality, Riemann—Liouville Fractional operator, generalizations. 
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     author = {M. Sofrani and A. Senusi},
     title = {Generalizations of some integral inequalities for {Riemann--Liouville} operator},
     journal = {\v{C}eby\v{s}evskij sbornik},
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M. Sofrani; A. Senusi. Generalizations of some integral inequalities for Riemann--Liouville operator. Čebyševskij sbornik, Tome 23 (2022) no. 2, pp. 161-169. http://geodesic.mathdoc.fr/item/CHEB_2022_23_2_a9/