Characterization of approximation schemes satisfying Shapiro’s Theorem

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

Fuzzy Best Simultaneous Approximation of a Finite Numbers of Functions

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

APPROXIMATION OF STOCHASTIC PARABOLIC DIFFERENTIAL EQUATIONS WITH TWO DIFFERENT FINITE DIFFERENCE SCHEMES

We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Uperieure S Ormale N Ecole Département De Mathématiques Et Applications Entropy Satisfying Ux Vector Splittings and Kinetic Bgk Models F. Bouchut Entropy Satisfying Ux Vector Splittings and Kinetic Bgk Models Entropy Satisfying Ux Vector Splittings and Kinetic Bgk Models

We establish forward and backward relations between entropy satisfying BGK models such as those introduced previously by the author and the rst order ux vector splitting numerical methods for systems of conservation laws. Classically, to a kinetic BGK model that is compatible with some family of entropies we can associate an entropy ux vector splitting. We prove that the converse is true: any e...