Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 541–555 | Cite as

Opial-Type Inequalities with Two Unknowns and Two Functions on Time Scales

  • Safi S. Rabie
  • Samir H. Saker
  • Donal O’Regan
  • Ravi P. AgarwalEmail author


In this paper, we prove some new Opial-type inequalities for two unknowns and general kernels on time scales. Also, we prove some new dynamic Opial-type inequalities of higher-order involving two different weight functions. The proofs use Hölder’s inequality, the reverse Hölder’s inequality, the chain rule, and a power rule of integration on time scales.


Opial’s inequality Time scales Hölder’s inequality 

Mathematics Subject Classification (2010)

26A15 26D10 26D15 39A13 34A40 


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  • Safi S. Rabie
    • 1
  • Samir H. Saker
    • 1
  • Donal O’Regan
    • 2
  • Ravi P. Agarwal
    • 3
    Email author
  1. 1.Department of Mathematics, Faculty of ScienceMansoura UniversityMansouraEgypt
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland
  3. 3.Department of MathematicsTexas A and M University-KingsvilleKingsvilleUSA

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