Krnic, M., Mikic, R., Pecaric, J. (2016). Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities. Advances in Operator Theory, 1(1), 104-122. doi: 10.22034/aot.1610.1040
Mario Krnic; Rozarija Mikic; Josip Pecaric. "Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities". Advances in Operator Theory, 1, 1, 2016, 104-122. doi: 10.22034/aot.1610.1040
Krnic, M., Mikic, R., Pecaric, J. (2016). 'Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities', Advances in Operator Theory, 1(1), pp. 104-122. doi: 10.22034/aot.1610.1040
Krnic, M., Mikic, R., Pecaric, J. Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities. Advances in Operator Theory, 2016; 1(1): 104-122. doi: 10.22034/aot.1610.1040
Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities
In this paper, we give converses of the Jensen and Edmundson-Lah-Ribaric 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 Holder and Hermite-Hadamard inequalities as well as for the inequalities of Giaccardi and Petrovic.