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By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.

In this work, an operator superquadratic function (in the sense) for positive Hilbert space operators is defined. Several examples with some important properties together observations which are related to convexity pointed out. A general Bohr’s inequality thus deduced. Jensen-type proved. Equivalent statements of a non-commutative version Jensen’s also established. Finally, several trace inequa...