Related papers: Means refinements via convexity
We define, in the frame of an abstract Wiener space, the notions of convexity and of concavity for the equivalence classes of random variables. As application we show that some important inequalities of the finite dimensional case have…
Harmonic, Geometric, Arithmetic, Heronian and Contraharmonic means have been studied by many mathematicians. In 2003, H. Evens studied these means from geometrical point of view and established some of the inequalities between them in using…
The secant method, as an important approach for solving nonlinear equations, is introduced in nearly all numerical analysis textbooks. However, most textbooks only briefly address the Q-order of convergence of this method, with few…
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…
In this paper, we describe a new vector similarity measure associated with a convex cost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle between the two surface normals is the…
Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper…
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
In this paper we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of operator Acz\'el inequality dealing with the weighted geometric mean.
For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on $\beta$ is determined so that $f$ is either starlike or convex of order $\alpha$. Several other…
For function of one variable, differentiability is equivalent to the existence of tangent line as the limit of secant line. The genuine counterpart of this equivalence for function of several variables is obtained for the first time.
In this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.
In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Renyi's…
In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
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.
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…
We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight…