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Opial Inequalities

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Dynamic Inequalities On Time Scales

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Abstract

In 1960 Opial proved that if x is absolutely continuous on [a, b] with \(x(a) = x(b) = 0,\) then

$$\displaystyle{ \int _{a}^{b}\left \vert x(t)\right \vert \left \vert x^{{{\prime}} }(t)\right \vert dt \leq \frac{\left (b - a\right )} {4} \int _{a}^{b}\left \vert x^{{{\prime}} }(t)\right \vert ^{2}dt. }$$
(3.0.1)

We refer the reader to [9] for results on Opial type inequalities.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University–Kingsville, Kingsville, TX, USA

    Ravi Agarwal

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

    Donal O’Regan

  3. Department of Mathematics, Mansoura University, Mansoura, Egypt

    Samir Saker

Authors
  1. Ravi Agarwal
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  2. Donal O’Regan
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  3. Samir Saker
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Agarwal, R., O’Regan, D., Saker, S. (2014). Opial Inequalities. In: Dynamic Inequalities On Time Scales. Springer, Cham. https://doi.org/10.1007/978-3-319-11002-8_3

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