Abstract

Using Hölder's inequality, the chain rule on time scales and the properties of geometrically convex and concave functions we prove some new dynamic inequalities and their converses on time scales. As a special case, we derive the classical Saitoh integral inequality.

Author information

Contact details are reproduced from the original publication and may be historical.

Donal O'Regan

School of Mathematics, National University of Ireland, Galway, Ireland

Samir H. Saker

Department of Mathematics, Faculty of Science, University of Mansoura, Egypt

S. S. Rabie

Department of Mathematics, Faculty of Science, University of Mansoura, Egypt

Ravi P. Agarwal

Department of Mathematics, Texas A&M University, Kingsville, TX 78363, U.S.A.

Ravi.Agarwal@tamuk.edu

Keywords

  • Opial's inequality
  • Saitoh's inequality
  • time scales
  • Hoelder's inequality

Mathematics Subject Classification

26A15, 26D10, 26D15, 39A13, 34A40

Suggested citation

D. O'Regan, S. H. Saker, S. S. Rabie, R. P. Agarwal. “Opial and Saitoh Type Inequalities on Time Scales.” Journal of Convex Analysis 27 (2020), No. 3, 1073–1090.

Copyright Heldermann Verlag 2020