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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.

We are given data α1, . . . , αm and a set of points E = {x1, . . . , xm}. In this paper we address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions f(xi) = αi, i = 1, . . . ,m, that is also n-convex on a set properly containing E. We consider both one point extensions of E, and extensions of E to all of IR. We also determine bounds on n-...