Related papers: Whitney-type estimates for convex functions
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization…
This paper studies the strong quasiconvexity of norm and distance functions in finite-dimensional normed spaces. Although the Euclidean norm is known to be strongly quasiconvex on bounded convex sets, a complete characterization of this…
In this article we utilise abstract convexity theory in order to unify and generalize many different concepts from nonsmooth analysis. We introduce the concepts of abstract codifferentiability, abstract quasidifferentiability and abstract…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.
The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illustrating the obtained results are included.
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.
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 analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
We introduce appropriate computable moduli of smoothness to characterize the rate of best approximation by multivariate polynomials on a connected and compact $C^2$-domain $\Omega\subset \mathbb{R}^d$. This new modulus of smoothness is…
We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
We prove a sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in a class of weighted Poincar\'e inequalities. The key point is the study of an optimal weighted Wirtinger inequality.
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
We study the boundary behaviour of a variant of the Fridman's invariant function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in $ \mathbb{C}^n $ and…