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

  • P. AgarwalEmail author
  • A. M. Jerbashian
  • J. E. Restrepo
Part of the Trends in Mathematics book series (TM)


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.


Integral inequalities Fractional integro-differentiation Weighted classes 

Mathematics Subject Classification Number:

26A33 35A23 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • P. Agarwal
    • 1
    • 2
    Email author
  • A. M. Jerbashian
    • 3
  • J. E. Restrepo
    • 4
  1. 1.Department of MathematicsAnand International College of EngineeringJaipurIndia
  2. 2.International Centre for Basic and Applied SciencesJaipurIndia
  3. 3.Institute of MathematicsUniversity of AntioquiaMedellinColombia
  4. 4.Regional CenterSouthern Federal UniversityRostovRussia

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