Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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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.

Time scales integral inequalities for superquadratic functions

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

Abstract

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