Showing papers in "Journal of Approximation Theory in 1989"

TL;DR: In this paper, the Ulam problem of finding conditions in order for a linear mapping near an approximately linear mapping to exist was solved and results involving a product of powers of norms were established.

TL;DR: The calculus of deterministic fractal functions is introduced in this article, which can be explicitly indefinitely integrated any number of times, yielding a hierarchy of successively smoother interpolation functions which generalize splines and which are attractors for iterated function systems.

TL;DR: In this article, the central theme of the work is the circle of ideas that relates total positivity to spherical series on the symmetric space GL(n, C ) U(n), and classical hypergeometric functions to hypergeometrical functions of matrix argument.

TL;DR: Generalisation du theoreme du point fixe de Dotson et application a l'approximation invariant as mentioned in this paper, and application invariance invariant to the application.

TL;DR: In this article, les operateurs integraux du type de Bernstein Mnf were defined, and the relation entre les derivees de Mnf, la vitesse d'approximation de Mn and la regularite de la fonction f was explored.

TL;DR: In this article, a set of nodes x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8, x 9, x 10, x 11, x 12, x 13, x 14, x 15, x 16, x 17, x 18, x 20, x 21, x 22, x 23, x 24, x 25, x 26, x 27, x 28, x 29, x 30, x n, x 31, x 32, x 33, x 34, x 35, x 36

TL;DR: In this paper, the possibilite d'approximation lineaire par morceaux d'une telle application fonction was studied, i.e.

TL;DR: On montre que la methode des moindres carres mobiles for l'interpolation multivariable peut etre placee dans le contexte de la theorie de Backus-Gilbert qui est elle-meme, au fond, une theorie d'interoperation as mentioned in this paper.

TL;DR: In this article, Cheng [J. Theory 39 (1983), 259−274] extended and sharpen Cheng's results for Bernstein polynomials to the Feller operator, where f is a function of bounded variation and the rates of convergence are determined by estimating ¦Ln(f, x) − f (x) in terms of certain bounds.

TL;DR: In this article, the authors consider l'espace des fonctions d'un espace de Hansdorff compact dans un espace lineaire norme and s'interesse a l'approximation simultanee de telles fonsctions, dans le sens de Tchebychev.

TL;DR: In this paper, the existence of selections continues for des applications a valeurs ensembles, and the authors propose a method for characterisation of ensemble selections based on characterisation.

TL;DR: In this article, an estimation de la vitesse de convergence des n-iemes operateurs de Meyer-Konig and de Zeller integres for les fonctions a variation bornee is presented.

TL;DR: In this article, the authors generalized Khan's result on equilibrium points of non-atomic games to a setting where agents' preferences need not be ordered and generalized it to the setting of nonatomic games.

TL;DR: In this paper, a classe d'operateurs d'approximation multivariables of Feller multivariable is defined, i.e., operateateurs with a constant constant.

TL;DR: It may be that a lattice is a useful structure for investigating and comparing smoothers, and a few related simple selectros are defined and investigated for this purpose.

TL;DR: In this paper, the authors present a characterization of generalized weighted Peetre K-functionals by means of a modulus of smoothness, which is based on the classical one taken on a certain linear transform of the function.

TL;DR: In this article, it was shown that for a compact absolutely convex subset of a normed space, the linear n -width obtained with the help of bounded linear rank n operators, the one obtained by arbitrary linear rank N operators, and the corresponing approximation number of the associated embedding all coincide.

TL;DR: It is shown that ifPM has a continuous selection, then it has one which is also homogeneous and additive modulo M and an analogous result holds if PM has a pointwise Lipschitz or Lipshitz continuous selection provided that M is complemented.

TL;DR: In this article, an optimal a posteriori parameter choice strategy for finite-dimensional approximations is developed for a general class of regularization methods for ill-posed linear operator equations.

TL;DR: Etude des meilleures bornes d'erreur d'interpolation par des fonctions splines du quatrieme degre. as discussed by the authors.

TL;DR: This paper proves that if Y is a closed subspace of the Banach space X, then L 1 ( μ , Y) is proximinal in L1 ( μ, X) if and only if L p is proximal in L p (μ, Y) for every p.

TL;DR: In this paper, it was shown that if all the partial derivatives of f of the first r orders exist and are continuous in S, then certain polynomials with integral coefficients, Bn, m(q, r−q), ef, converge to ( ∂ r ∂x q ∂y r − q )(Bn,mf) with each coefficient replaced by its integral part.

TL;DR: For a closed subspace Y of a real Banach space and (Ω, μ) a finite measure space, the main result of as discussed by the authors is that Lφ(μ, Y) is proximinal if and only if

TL;DR: In this article, the determination des vitesses de convergence for les fonctions continues and discontinues a variation bornee Inegalite de type Cheney-Sharma, which is a variation of the Inegalitic version of the CheneySharma.

TL;DR: On etend aux espaces uniformement convex quelques theoremes d'Angelos-Egger-Smarzewski relatifs a la meilleure approximation fortement unique as discussed by the authors.

TL;DR: In this article, the Lp-convergence des processus interpolatoires d'Hermite sur des nœuds de Tchebychev is discussed, and the degre d'approximation d'une fonction continue donnee par des Processus Interpreters d'HERMITE.

TL;DR: In this paper, an existence theorem for a best approximation to a function in L p, 1 ⩽ p �, by functions from a nonconvex set is established under certain general conditions on the set.

TL;DR: In this paper, the structure de l'erreur d'approximation par des polynomes algebriques is studied, based on Gonska-Hinnemann-Yu method.