In this paper, we consider double sequence iteration processes for strongly $rho$-contractive mapping in modular space. It is proved, these sequences, convergence strongly to a fixed point of the strongly $rho$-contractive mapping.

In this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete CAT(0) space for SP-iterative process and Thianwan's iterative process.

Diagonal dominant implicit-difference schemes approximating a porous media type class of multidimensional nonlinear equations are shown to generate semigroups in an approximate l) -space, and the rate of convergence to the semigroup solution in Ll is given. The numerical schemes proposed by Berger et al. in [4] are described and a proof of convergence for the fully discrete algorithms is outlin...

We show that the space Lip0(R) is the dual space of L(R;R)/N where N is the subspace of L(R;R) consisting of vector fields whose divergence vanishes identically. We prove that although the quotient space L(R;R)/N is weakly sequentially complete, the subspace N is not nicely placed in other words, its unit ball is not closed for the topology τm of local convergence in measure. We prove that if Ω...

We study the asymptotic behavior, at small viscosity ε, of the NavierStokes equations in a 2D curved domain. The Navier-Stokes equations are supplemented with the slip boundary condition, which is a special case of the Navier friction boundary condition where the friction coefficient is equal to two times the curvature on the boundary. We construct an artificial function, which is called a corr...

L 2 boundary decay properties of the heat kernel and spectral density. We deduce bounds on the rate of convergence of the eigenvalues when the region is slightly reduced in size. It is remarkable that several of the bounds do not involve the space dimension. AMS subject classifications: 35P99, 35P20, 47A75, 47B25 keywords: boundary decay, Laplacian, Hardy inequality, eigenfunctions, heat kernel...

Abstract. Invariance principle in L(0, 1) is studied using signed random measures. This approach to the problem uses an explicit isometry between L(0, 1) and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a L(0, 1) version of the invariance principle in the case of...

For $l$-homogeneous linear differential operators $\mathcal{A}$ of constant rank, we study the implication $v_j\rightharpoonup v$ in $X$ and $\mathcal{A} v_j\rightarrow \mathcal{A} $W^{-l}Y$ implies $F(v_j)\rightsquigarrow F(v)$ $Z$, where $F$ is an $\mathcal{A}$-quasiaffine function $\rightsquigarrow$ denotes appropriate type weak convergence. Here $Z$ a local $L^1$-type space, either space $\...