The convergence in meaaa of a veighted sum k a.k(Xk EXk) of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the {a.. }-compactly uniform integrability of {X. }. This condition, which is implied by the tightness of {X,,} and the {a,,k }-uniform integrability of {[IX,, II}, is weaker than the...

Uniform tf(h2) convergence is proved for the El-Mistikawy-Werle discretization of the problem —eu" + au' + bu = f on (0,1), u(0) = A, u(l) = B, subject only to the conditions a, b, f e ^r2'oo[0,1] and a(x) > 0, 0 < i < 1. The principal tools used are a certain representation result for the solutions of such problems that is due to the author [Math. Comp., v. 48, 1987, pp. 551-564] and the gener...

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

In [C2], Chemin shows that solutions of the Navier-Stokes equations in R for an incompressible fluid whose initial vorticity lies in L ∩ L∞ converge in the zero-viscosity limit in the L–norm to a solution of the Euler equations, convergence being uniform over any finite time interval. In [Y2], Yudovich assumes an initial vorticity lying in L for all p ≥ p0, and establishes the uniqueness of sol...

In all of these theorems the notion of convergence used in (1-1) and (1-2) has essentially been strong convergence. It is the purpose of the present paper to prove analogous theorems for a certain class of notions of convergence, which will include, in the case of Banach spaces of functions with the sup norm, bounded, pointwise convergence, and convergence of bounded sequences which is uniform ...

We derive new representations for the generalised Jacobian of a locally Lipschitz map between finite dimensional real Euclidean spaces as lower limit (i.e., inferior) classical derivative where it exists. The lead to significantly shorter proofs basic properties subgradient and including chain rule. establish that sequence maps converges given in L-topology—that is, weakest refinement sup norm ...

in this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎fredholm-volterra integral equations (fvies) are smooth‎.