Jensen’s Operator Inequality for Strongly Convex Functions
نویسنده
چکیده
We give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve Hölder-McCarthy inequality under suitable conditions. More precisely we show that if Sp (A) ⊂ I ⊆ (1,∞), then 〈Ax, x〉 r ≤ 〈Ax, x〉 − r − r 2 (
منابع مشابه
JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS
In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.
متن کاملInequalities of Ando's Type for $n$-convex Functions
By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
متن کاملThis is a submission to one of journals of TMRG: BJMA/AFA EXTENSION OF THE REFINED JENSEN’S OPERATOR INEQUALITY WITH CONDITION ON SPECTRA
We give an extension of the refined Jensen’s operator inequality for n−tuples of self-adjoint operators, unital n−tuples of positive linear mappings and real valued continuous convex functions with conditions on the spectra of the operators. We also study the order among quasi-arithmetic means under similar conditions.
متن کاملA REFINEMENT OF JENSEN’S INEQUALITY WITH APPLICATIONS FOR f-DIVERGENCE MEASURES
A refinement of the discrete Jensen’s inequality for convex functions defined on a convex subset in linear spaces is given. Application for f -divergence measures including the Kullback-Leibler and Jeffreys divergences are provided as well.
متن کاملJensen’s Inequality for g-Convex Function under g-Expectation
A real valued function defined on R is called g–convex if it satisfies the following “generalized Jensen’s inequality” under a given g-expectation, i.e., h(E[X ]) ≤ E[h(X)], for all random variables X such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient conditions for a C-function being g-convex. We also studied some more general situation...
متن کامل