Related papers: Method of Separating Tangents
In this paper we consider the variable inequality problem, that is, to find a solution of the inclusion given by the sum of a function and a point-to-cone application. This problem can be seen as a generalization of the classical system…
Jensen's Inequality (JIEQ) has proved to be a major tool to prove the consistency of various fluctuation theorems with the second law in microscopic thermodynamics. We show that the situation is far from clear and the reliance on the JIE…
The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well…
Bell inequalities are derived for any number of observers, any number of alternative setups for each one of them, and any number of distinct outcomes for each experiment. It is shown that if a physical system consists of several distant…
Consider a semi-algebraic function $f\colon\mathbb{R}^n \to {\mathbb{R}},$ which is continuous around a point $\bar{x} \in \mathbb{R}^n.$ Using the so--called {\em tangency variety} of $f$ at $\bar{x},$ we first provide necessary and…
Given a function f in the exterior of a convex curve in the real plane, we prove that if the restrictions of f to the tangent lines to the curve extend as entire functions, then the function f is an entire function of two variables.
We have recently established some integral inequalities for convex functions via the Hermite-Hadamard's inequalities. In continuation here, we also establish some interesting new integral inequalities for convex functions via the…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
Convexity is a key concept in information theory, namely via the many implications of Jensen's inequality, such as the non-negativity of the Kullback-Leibler divergence (KLD). Jensen's inequality also underlies the concept of Jensen-Shannon…
In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…
The problem on the minimal number (with respect to deformation) of intersection points of two closed curves on a surface is solved. Following the Nielsen approach, we define classes of intersection points and essential classes of…
We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded…
Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error…
In this paper, we state some characterizations of $h$-convex function is defined on a convex set in a linear space. By doing so, we extend the Jensen-Mercer inequality for $h$-convex function. We will also define $h$-convex function for…
In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type…
Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von…
In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
For a real-valued non-negative and log-concave function we introduce a notion of difference function; the difference function represents a functional analog on the difference body of a convex body. We prove a sharp inequality which bounds…
We consider the large deviations associated with the empirical mean of independent and identically distributed random variables under a subexponential moment condition. We show that non-trivial deviations are observable at a subexponential…