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Advances in Mathematical Inequalities and Applications pp 199–217Cite as

Birkhäuser

Weighted Integral Inequalities in Terms of Omega-Fractional Integro-Differentiation

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Near Kanota, Agra Road, Jaipur, 303012, Rajasthan, India

    P. Agarwal

  2. International Centre for Basic and Applied Sciences, Jaipur, India

    P. Agarwal

  3. Institute of Mathematics, University of Antioquia, Cl. 53 - 108, Medellin, Colombia

    A. M. Jerbashian

  4. Regional Center, Southern Federal University, Rostov, Russia

    J. E. Restrepo

Authors
  1. P. Agarwal
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  2. A. M. Jerbashian
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  3. J. E. Restrepo
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Corresponding author

Correspondence to P. Agarwal .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, India

    Praveen Agarwal

  2. Department of Mathematics, Victoria University, Melbourne, VIC, Australia

    Silvestru Sever Dragomir

  3. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mohamed Jleli

  4. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Bessem Samet

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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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