J. Korean Math. Soc. 2013; 50(3): 465-477
Printed May 1, 2013
https://doi.org/10.4134/JKMS.2013.50.3.465
Copyright © The Korean Mathematical Society.
Josipa Bari\'{c}, Rabia Bibi, Martin Bohner, and Josip Pe\v{c}ari\'{c}
University of Split, National University of Sciences and Technology, Missouri University of Science and Technology, University of Zagreb
In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals.
Keywords: time scales, superquadratic functions, Jensen's inequality, H\"older's inequality, Minkowski's inequality, Jessen--Mercer's inequality, Slater's inequality, Hermite--Hadamard's inequality
MSC numbers: Primary 26D15, 26D20, 26D99, 34N05
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