Converses of convex inequalities in Hilbert space

On some new converses of convex inequalities in Hilbert space

“…Our first result is a refinement of the converse of Jensen's inequality (1.4) for selfadjoint operators obtained in [7].…”

“…In order to obtain a converse of the Lah-Ribarič inequality for convex functions (1.6), we need the following result found in [7]:…”

“…R. Jakšic and J. Pečarić in their paper [7] gave the following result, which concerns the difference between the right and the left side of the Mond-Pečarić inequality (1.3).…”

“…Remark 1.5. One can see that if in Theorem 1.4 we choose The authors in [7] also gave a series of inequalities that concerns with the difference between the right and the left side of the inequality (1.5), which we state below.…”

“…The main aim of this paper is to give refinements and improvements of converses of the Jensen inequality (1.4) and the scalar Lah-Ribarič inequality (1.6) for selfadjoint operators obtained in [7].…”