Mond-Pecaric Method in Operator Inequalities

By T. Furuta, J. Mićić, Josip E. Pecaric, Y. Seo. 2005

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Jensen's operator inequality and its converses (2006, background): “Numerous applications of the previous theorem can be given (see [9]).”
Čebyšev's type inequalities for functions of selfadjoint operators in Hilbert spaces (2010, background): “For a recent monograph devoted to various inequalities for functions of selfadjoint operators, see [12] and the references therein.”
A variant of Jensen’s inequality of Mercer’s type for operators with applications (2006, methodology): “In the same way as in (i) Step 2 we obtain inequality (5).”
Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces (2012, background): “1) hf (A)x; xi M hAx; xi M m f (m) + hAx; xi m M m f (M) for each x 2 H with kxk = 1: For a recent monograph devoted to various inequalities for functions of selfadjoint operators, see [10] and the references therein.”
Refinements of the operator Jensen-Mercer inequality (2013, background): “Several versions of the Jensen operator inequality can be found in [6, 8].”