Strengthened converses of the Jensen and Edmundson- Lah-Ribarič inequalities (CROSBI ID 233183)
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Krnić, Mario ; Mikić, Rozarija ; Pečarić, Josip
engleski
Strengthened converses of the Jensen and Edmundson- Lah-Ribarič inequalities
In this paper, we give converses of the Jensen and Edmundson-Lah-Ribari\v{; ; ; c}; ; ; inequalities which are more accurate than the existing ones. These converses are given in a difference form and they rely on the recent refinement of the Jensen inequality obtained via linear interpolation of a convex function. As an application, we also derive improved converse relations for generalized means, for the H\"{; ; ; o}; ; ; lder and Hermite-Hadamard inequalities as well as for the inequalities of Giaccardi and Petrovi\'{; ; ; c}; ; ; .
positive linear functional ; convex function ; converse ; Jensen inequality ; Edmundson-Lah-Ribari\v{; ; ; c}; ; ; inequality
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