Mohammad W. Alomari
Published 2016-09-20Version 1
In this work, several sharp bounds for the \v{C}eby\v{s}ev functional involving various type of functions are proved. In particular, for the \v{C}eby\v{s}ev functional of two absolutely continuous functions whose first derivatives are both convex, convex and belong to $L_p$-spaces, convex and bounded variation, convex and Lipschitz mappings new sharp bounds are presented. Other related results regarding two convex and concave functions are given.
$L_p$-Bounds for the Čebyšev functional
Some New Inequalities for (h-s)_{1,2}-convex Functions via Further Properties
Levin Steckin theorem and inequalities of the Hermite-Hadamard type
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