Related papers: Some Generalizations of Jensen's Inequality

We offer a new proof of uniform convexity inequalities for the Finsler manifold of nonpositive curvature taken on the space of positive-semidefinite matrices with the weighted matrix geometric mean defining the geodesic between two points.…

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or free energy function…

In this note we describe some results concerning upper and lower bounds for the Jensen functional. We use several known and new results to shed light on the concepts of superterzatic functions.

Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.

In recent study of partial differential equations (PDEs) with random initial data and singular stochastic PDEs with random forcing, it is essential to study the regularity property of various stochastic objects. These stochastic objects are…

We extend ideas of Garling to consider the so called Hardy martingales in a more general setting of H^p theory of compact abelian groups with ordered dual. As a consequence, we obtain a new proof of a result of Helson and Lowdenslager which…

The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up. This quantity, in contrast to the remaining Jensen divergences, is very sensitive to the fluctuations of the…

We establish various extensions of the convexity Dines theorem for a (joint-range) pair of inhomogeneous quadratic functions. If convexity fails we describe those rays for which the sum of the joint-range and the ray is convex. These…

In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.

We study the power mean inequality of the generalized trigonometric and hyperbolic functions with two parameters. The generalized $p$-trigonometric and $(p, q)$-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi,…

In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.

We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

This expository paper presents elementary proofs of four basic results concerning derivatives of quasi-convex functions. They are combined into a fifth theorem which is simple to apply and adequate in many cases. Along the way we establish…

As established by R T. Rockafellar, real valued convex-concave functions are generically differentiable. It this paper we shall show that for a convex-concave function defined on an open convex set $C \times D,$ there exist dense subsets…

This paper studies the log-convexity of the extended beta functions. As a consequence, Tur\'an-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the…

We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with…

In this paper, a new class of convex functions as a generalization of convexity which is called (h-m)-convex functions and some properties of this class is given. We also prove some Hadamard's type inequalities.

In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backward doubly stochastic variational…