On simultaneous Chebyshev approximation in the ‘‘sum” norm

On nonlinear simultaneous Chebyshev approximation problems ✩

This paper is concerned with the problem of nonlinear simultaneous Chebyshev approximation in a real continuous function space. Some results on existence are established, in addition to characterization conditions of Kolmogorov type and also of alternation type. Applications are given to approximation by rational functions, by exponential sums and by Chebyshev splines with free knots.  2003 El...

On Reverse Chebyshev Approximation

We investigate the problem of determining the largest domain where given error bounds can be satissed by an approximation of a given continuous real valued real function using polynomials of several kinds. Since the the error bounds are xed and the domain is variable we call this problem reverse Chebyshev approximation.

Rational Chebyshev Approximation on the Unit Disk

In a recent paper we showed that er ror curves in po lynomia l Chebyshev a p p r o x i m a t i o n of ana ly t ic functions on the unit disk tend to a p p r o x i m a t e perfect circles abou t the origin [23]. M a k i n g use of a theorem of Ca ra th6odo ry and Fej6r, we der ived in the process a me thod for calculat ing near-bes t a p p r o x i m a t i o n s rapid ly by finding the pr incipal...

Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules

A NORM INEQUALITY FOR CHEBYSHEV CENTRES

In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice functi...