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2016•Electronic Journal of Linear AlgebraOpen access

Cyclic Refinements of the Different Versions of Operator Jensen's Inequality

László Horváth, Khuram Ali Khan, ‎Josip Pečarić

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Abstract

Refinements of the operator Jensen's inequality for convex and operator convex functions are given by using cyclic refinements of the discrete Jensen's inequality. Similar refinements are fairly rare in the literature. Some applications of the results to norm inequalities, the Holder McCarthy inequality and generalized weighted power means for operators are presented.

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Refinements of the operator Jensen's inequality for convex and operator convex functions are given by using cyclic refinements of the discrete Jensen's inequality. Similar refinements are fairly rare in the literature. Some applications of the results to norm inequalities, the Holder McCarthy inequality and generalized weighted power means for operators are presented.

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Available abstract

Refinements of the operator Jensen's inequality for convex and operator convex functions are given by using cyclic refinements of the discrete Jensen's inequality. Similar refinements are fairly rare in the literature. Some applications of the results to norm inequalities, the Holder McCarthy inequality and generalized weighted power means for operators are presented.

Key concepts: Jensen's inequality, Mathematics, Inequality of arithmetic and geometric means, Log sum inequality, Kantorovich inequality, Convex function, Inequality, Operator (biology)

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