Abstract
Some generalizations of fractional integro-differentiation operators containing a functional parameter \(\omega \) are introduced. These operators are used to get some new inequalities including \(\omega \)-weighted Pólya–Szegö type inequalities, \(\omega \)-weighted Chebyshev-type integral inequalities, \(\omega \)-weighted Minkowskis reverse integral inequalities, \(\omega \)-weighted Hölder reverse integral inequalities, \(\omega \)-weighted integral inequalities for arithmetic and geometric means. The majority of the obtained inequalities becomes the classical or the well-known ones in some particular cases of the weights.
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Agarwal, P., Jerbashian, A.M., Restrepo, J.E. (2018). Weighted Integral Inequalities in Terms of Omega-Fractional Integro-Differentiation. In: Agarwal, P., Dragomir, S., Jleli, M., Samet, B. (eds) Advances in Mathematical Inequalities and Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-3013-1_10
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DOI: https://doi.org/10.1007/978-981-13-3013-1_10
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