In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points Xn := {xi}ni=0 in R, the barycentric approximation of a convex function f is of the form:

let $omega_x$ be a bounded, circular and strictly convex domain of a banach space $x$ and $mathcal{h}(omega_x)$ denote the space of all holomorphic functions defined on $omega_x$. the growth space $mathcal{a}^omega(omega_x)$ is the space of all $finmathcal{h}(omega_x)$ for which $$|f(x)|leqslant c omega(r_{omega_x}(x)),quad xin omega_x,$$ for some constant $c>0$, whenever $r_{omega_x}$ is the m...

The paper is motivated by the study of graded representations of Takiff algebras, cominuscule parabolics, and their generalizations. We study certain special subsets of the set of weights (and of their convex hull) of the generalized Verma modules (or GVM’s) of a semisimple Lie algebra g. In particular, we extend a result of Vinberg and classify the faces of the convex hull of the weights of a ...

Different methods have been used in studying the univalence of the integral (1) Jα,β(f)(z) = ∫ z 0 ( f ′(t) )α(f(t) t )β dt, α, β ∈ R, where f belongs to one of the known families of holomorphic and univalent functions f(z) = z + a2z + · · · in the unit disk D = {z : |z| < 1} (see [5]). In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains ...

Constrained multidimensional patterns differ from the well known frequent patterns from a conceptual and logical points of view because they are structured and support various types of constraints. Classical data mining techniques are based on the power set lattice and, even extended, are not suitable when addressing the discovery of multidimensional patterns. In this paper we propose a foundat...

Our main interest in this paper is approximation of a continuous function, on a finite interval, which changes convexity finitely many times by algebraic polynomials which are coconvex with it. This topic has received much attention in recent years, and the purpose of this paper is to give final answers to open questions concerning the validity of Jackson type estimates involving the weighted D...

Convex polytopes are the d-dimensional analogues of 2-dimensional convex polygones and 3-dimensional convex polyhedra. A polytope is a bounded convex set in R d that is the intersection of a finite number of closed halfspaces. The faces of a polytope are its intersections with supporting hyperplanes. The/-dimensional faces are called the i-faces and f i ( P ) denotes the number of i-faces of a ...

Let Xn := {xi}ni=0 be a given set of (n + 1) pairwise distinct points in R (called nodes or sample points), let P = conv(Xn), let f be a convex function with Lipschitz continuous gradient on P and λ := {λi}ni=0 be a set of barycentric coordinates with respect to the point set Xn. We analyze the error estimate between f and its barycentric approximation:

Constrained multidimensional patterns differ from the well-known frequent patterns from a conceptual and logical points of view because they are provided with a common structure and support various types of constraints. Classical data mining techniques are based on the power set lattice of binary attributes and, even extended, are not suitable when addressing the discovery of constrained multid...

‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...