Journal of Convex Analysis 27 (2020), No. 3, 1073--1090
Copyright Heldermann Verlag 2020
Opial and Saitoh Type Inequalities on Time Scales
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
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.
Keywords: Opial's inequality, Saitoh's inequality, time scales, Hoelder's inequality.
MSC: 26A15, 26D10, 26D15, 39A13, 34A40.
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