Advances in Difference Equations (Aug 2019)

On some generalizations of dynamic Opial-type inequalities on time scales

  • Fatma M. KH,
  • A. A. El-Deeb,
  • A. Abdeldaim,
  • Zareen A. Khan

DOI
https://doi.org/10.1186/s13662-019-2268-0
Journal volume & issue
Vol. 2019, no. 1
pp. 1 – 14

Abstract

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Abstract In this paper, we prove some new generalizations of dynamic Opial-type inequalities on time scales. From these inequalities, as special cases, we formulate some integral and discrete inequalities proved in the literature and also extend some obtained dynamic inequalities on time scales. The main results are proved by using some algebraic inequalities, Hölder’s inequality, and a simple consequence of Keller’s chain rule on time scales.