Refined converses of Jensen's inequality for operators

DOI10.1186/1029-242X-2013-353zbMath1298.47026WikidataQ59299529 ScholiaQ59299529MaRDI QIDQ2437663

Jadranka Mićić, Jurica Perić, Josip E. Pečarić

Publication date: 13 March 2014

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

convex functionself-adjoint operatorpositive linear mappingconverse of Jensen's operator inequalityMond-Pečarić method

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Equations involving linear operators, with operator unknowns (47A62) Convexity of real functions in one variable, generalizations (26A51) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (4)

More precise estimates for the Jensen operator inequality obtained via the Lah-Ribarič inequality ⋮ Some complementary inequalities to Jensen's operator inequality ⋮ An interpolation of Jensen's inequality and its converses with applications to quasi-arithmetic mean inequalities ⋮ On Levinson's operator inequality and its converses

Cites Work

• Some further refinements and extensions of the Hermite-Hadamard and Jensen inequalities in several variables
• A new refinement of Jensen's inequality in linear spaces with applications
• Jensen's inequality for operators without operator convexity
• Further refinements of the Jensen inequalities based upon samples with repetitions
• Jensen's inequality for operators and Loewner's theorem
• JENSEN'S OPERATOR INEQUALITY

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