Inequalities of convex functions and self-adjoint operators. (English) Zbl 1300.47025

Summary: The paper offers generalizations of the Jensen-Mercer inequality for self-adjoint operators and generally convex functions. The obtained results are applied to define the quasi-arithmetic operator means without using operator convexity. The version of the harmonic-geometric-arithmetic operator mean inequality is derived as an example.


47A63 Linear operator inequalities
39B62 Functional inequalities, including subadditivity, convexity, etc.
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