On Dependence of Sets of Functions on the Mean Value of their Elements
Journal Title: Mathematical Modelling and Analysis - Year 2009, Vol 14, Issue 1
Abstract
The paper considers, for a given closed bounded set $Msubset {mathbb R}^m$ and $K=(0,1)^nsubset {mathbb R}^n$, the set ${mathcal M}= { hin L_2(K;{mathbb R}^m)mid h(x) in M,,a.e.,xin K}$ and its subsets [ {mathcal M}(hat h)=Big{ hin {mathcal M}mid int _K h(x)dx =hat h Big}. ] It is shown that, if a sequence ${ hat h_k} subset coM $ converges to an element $h_0$. $h_k in mathcal{M}(hat h_k)$ there is $h_k^{‘} in mathcal{M}(hat h_0)$ such that $h_k^{‘}-h_k rightarrow 0$ as $k rightarrow infty$. If, in addition, the set $M$ is finite or $M$ is the convex hull of a finite set of elements, then the multivalued mapping $hat h rightarrow {mathcal M}(hat h)$ is lower semicontinuous on $coM$.
Authors and Affiliations
U. Raitums
Keywords
Related Articles
- EP ID EP83039
- DOI 10.3846/1392-6292.2009.14.91-98
- Views 94
- Downloads 0
Construction of Chaotic Dynamical System
The first-order difference equation x[i][sub]n[/sub][/i][sub]+1[/sub] = [i]f [/i](x[i][sub]n[/sub][/i]),[i] n[/i] = 0, 1, . . ., where [i]f[/i] : R → R, is referred as an one-dimensional discrete dynamical system. If fun...
A Separation Principle of Time-Varying Dynamical Systems: A Practical Stability Approach
In this paper we treat the problem of practical feedback stabilization for a class of nonlinear time-varying systems by means of an observer. A separation principle is given under a restriction about the perturbed term t...
A Quasistatic Unilateral Contact Problem with Friction for Nonlinear Elastic Materials
The aim of this paper is to prove the existence of a solution to the quasistatic unilateral contact problem with a modified version of Coulomb's law of dry friction for nonlinear elastic materials. We derive a variationa...
Unsteady Squeezing Flow of a Viscous MHD Fluid Between Parallel Plates, a Solution Using the Homotopy Perturbation Method
The present paper analyses the unsteady 2-dimensional flow of a viscous MHD fluid between two parallel infinite plates. The two infinite plates are considered to be approaching each other symmetrically, causing the squee...
On Dependence of Sets of Functions on the Mean Value of their Elements
The paper considers, for a given closed bounded set $Msubset {mathbb R}^m$ and $K=(0,1)^nsubset {mathbb R}^n$, the set ${mathcal M}= { hin L_2(K;{mathbb R}^m)mid h(x) in M,,a.e.,xin K}$ and its subsets [ {mathcal M}(hat...