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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Safi S. Rabie & Samir H. Saker

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  3. Department of Mathematics, Texas A and M University-Kingsville, Kingsville, TX, 78363, USA

    Ravi P. Agarwal

Authors
  1. Safi S. Rabie
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  2. Samir H. Saker
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  3. Donal O’Regan
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  4. Ravi P. Agarwal
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Correspondence to Ravi P. Agarwal.

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Rabie, S.S., Saker, S.H., O’Regan, D. et al. Opial-Type Inequalities with Two Unknowns and Two Functions on Time Scales. Vietnam J. Math. 44, 541–555 (2016). https://doi.org/10.1007/s10013-015-0169-4

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  • DOI: https://doi.org/10.1007/s10013-015-0169-4

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