We prove that the Ciarlet-Nečas non-interpenetration of matter condition [9] can be extended to the case of SBV -deformations of hyperelastic brittle materials, and can be taken into account for some variational models in fracture mechanics. In order to formulate such a condition, we define the deformed configuration under an SBV -map by means of the approximately differentiable representative,...

We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.

We prove global stability results of DiPerna-Lions renormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which includes the so-called Maxwell boundary conditions, and we prove that it is realized (it is not only a bounda...

the aim of this paper is to study the behaviour of certain sequence of nonlinear durrmeyer operators $nd_{n}f$ of the form $$(nd_{n}f)(x)=intlimits_{0}^{1}k_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{n}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% k_{n}left( x,t,uright) $ satisfies some suitable assumptions. here we estimate the rate...

The basic concept of multi-dimensional limiting process (MLP) on unstructured grids is inherited and modified for improving shock stabilities and reducing numerical dissipation on smooth regions. A relaxed version of MLP condition, simply named as weak-MLP, is proposed for reducing dissipation. Moreover, a stricter condition, that is the strict-MLP condition, is proposed to enhance the numerica...

The aim of this paper is to investigate the weak convergence for negatively associated random #elds. To this end, we obtain some moment inequalities for the maximum of partial sums for a negatively associated random #eld, which also are of independent interest. c © 2001 Elsevier Science B.V. All rights reserved MSC: primary 60F05; secondary 62E20

We present a random probability distribution which approximates, in the sense of weak convergence, the Dirichlet process and supports a Bayesian resampling plan called a proper Bayesian bootstrap. 2000 Mathematics Subject Classification: 62G09, 60B10.

The asymptotic validity of tests is usually established by making appropriate primitive assumptions, which imply the weak convergence of a specific function of the data, and an appeal to the continuous mapping theorem. This paper, instead, takes the weak convergence of some function of the data to a limiting random element as the starting point, and studies efficiency in the class of tests that...

In this paper, we propose a new proximal gradient method for convex minimization problem in real Hilbert spaces. We suggest linesearch which does not require the condition of Lipschitz constant and improve conditions inertial term speed up performance convergence. Moreover, prove weak convergence proposed under some suitable conditions. The numerical implementations data classification are repo...