相关论文: Jensen's trace inequality in several variables
We prove a matrix trace inequality for completely monotone functions and for Bernstein functions. As special cases we obtain non-trivial trace inequalities for the power function x->x^q, which for certain values of q complement McCarthy's…
Jensen's inequality, attributed to Johan Jensen -- a Danish mathematician and engineer noted for his contributions to the theory of functions -- is a ubiquitous result in convex analysis, providing a fundamental lower bound for the…
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's…
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
Jensen's inequality is ubiquitous in measure and probability theory, statistics, machine learning, information theory and many other areas of mathematics and data science. It states that, for any convex function $f\colon K \to \mathbb{R}$…
In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…
We develop a new framework for the Jensen-type inequalities that allows us to deal with functions not necessarily convex and Borel measures not necessarily positive.
In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.
It is shown in this paper that two positive elements of a C*-algebra agree on all lower semicontinuous traces if and only if they are equivalent in the sense of Cuntz and Pedersen. A similar result is also obtained in the more general case…
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…
Some inequalities for different types of convexity are established.
Given a function $f$ defined on a nonempty and convex subset of the $d$-dimensional Euclidean space, we prove that if $f$ is bounded from below and it satisfies a convexity-type functional inequality with infinite convex combinations, then…
In this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.
We show that if $f$ is a non-negative superquadratic function, then $A\mapsto\mathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr f\left( {\frac{{A + B}}{2}} \right) +\tr f\left(\left|…
In this work, new inequalities connected with the Steffensen's integral inequality for s-convex functions are proved
Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.
In this paper, some Jensen's type inequalities between quaternionic bounded selfadjoint operators on quaternionic Hilbert spaces are proved, using a log-convex function. Also, by applying a specific log-convex function, some particular…
In this paper the Jessen's type inequality for normalized positive $C_0$-semigroups is obtained. An adjoint of Jessen's type inequality has also been derived for the corresponding adjoint-semigroup, which does not give the analogous results…
Problems pointwise estimates from above functions or its averages often arise in the function theory under known integral restrictions on the growth of this function. We offer an approach to such problems based on the integral Jensen's…
We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving…