Generalizations of some integral inequalities for Riemann–Liouville operator
https://doi.org/10.22405/2226-8383-2022-23-2-161-169
Abstract
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 𝐼𝛼, were established and proved some new integral inequalities for the Chebyshev fonctional
$$𝑇(𝑓, 𝑔) :=1/(𝑏 − 𝑎)∫︁𝑎𝑏 𝑓(𝑥)𝑔(𝑥)𝑑𝑥 −1/(𝑏 − 𝑎)∫︁𝑎𝑏 𝑓(𝑥)𝑑𝑥 1/(𝑏 − 𝑎)∫︁ 𝑎𝑏 𝑔(𝑥)𝑑𝑥.$$
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.
About the Authors
Mohammed Sofrani
University of Tiaret
Algeria
Algeria
Laboratory of informatics and mathematics
Abdelkader Senouci
University of Tiaret
Algeria
Algeria
professor, laboratory of informatics and mathematics
References
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Review
For citations:
Sofrani M., Senouci A. Generalizations of some integral inequalities for Riemann–Liouville operator. Chebyshevskii Sbornik. 2022;23(2):161-169. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-2-161-169
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