More accurate classes of Jensen-type inequalities for convex and operator convex functions (CROSBI ID 243759)
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Podaci o odgovornosti
Choi, Daeshik ; Krnić, Mario ; Pečarić, Josip
engleski
More accurate classes of Jensen-type inequalities for convex and operator convex functions
Motivated by a recent refinement of the scalar Jensen inequality obtained via linear interpolation, in this paper we develop a general method for improving two classes of Jensen-type inequalities for bounded self-adjoint operators. The first class refers to a usual convexity, while the second one deals with the operator convexity. The general results are then applied to quasi-arithmetic and power operator means. As a consequence, we obtain strengthened forms of the inequalities between arithmetic, geometric and harmonic operator means. We also obtain more accurate Young-type inequalities for unitarily invariant norms as well as more precise relations for some important jointly concave mappings.
Jensen inequality, Young inequality, convexity, operator convexity, operator mean, refinement
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Podaci o izdanju
21 (2)
2018.
301-321
objavljeno
1331-4343
10.7153/mia-2018-21-22