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Inequalities of the Edmundson-Lah-Ribarič type for selfadjoint operators in Hilbert spaces

By exploiting some scalar inequalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Jensen's inequality and in the Edmundson-Lah-Ribarič inequality for selfadjoint operators in Hilbert space that hold for the class of $n$-convex functions. As an application, main results are applied to quasi-arithmetic operator means, with a particular emphasis to power operator means.

Jensen inequality ; Edmundson-Lah-Ribarič inequality ; n-convex functions ; divided differences ; scalar product ; means

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