In this paper we study some new converses of the operator version for the Jensen inequality and the scalar Lah--Ribarič inequality for continuous convex functions and we will give applications of those results to quasi-arithmetic means and power means for selfadjoint operators. Furthermore, we will also give improvements of the obtained results.
"On some new converses of convex inequalities in Hilbert space." Banach J. Math. Anal. 9 (2) 63 - 82, 2015. https://doi.org/10.15352/bjma/09-2-6