Some better bounds in converses of the Jensen operator inequality (Q2914876)
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scientific article; zbMATH DE number 6084698
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some better bounds in converses of the Jensen operator inequality |
scientific article; zbMATH DE number 6084698 |
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Some better bounds in converses of the Jensen operator inequality (English)
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21 September 2012
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convex function
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Jensen's operator inequality
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Mond-Pečarić method
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selfadjoint operators
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positive linear mapping
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0.94089675
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0.9394325
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0.9374932
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0.9347298
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0.9274173
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0.9195286
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Inspired by a version of Jensen's operator inequality without operator convexity due to the authors of the present paper [Linear Algebra Appl. 434, No. 5, 1228--1237 (2011; Zbl 1216.47026)], the authors study converses of a generalized Jensen's inequality for a continuous field of self-adjoint operators, a unital field of positive linear mappings and real valued continuous convex functions. They give the difference and ratio type converses and provide a refined calculation of bounds in the case of power functions.
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