When an approximant is accurate on interval, it only natural to try extend multi-dimensional domains. In the present article we make use of fact that linear rational barycentric interpolants converge rapidly toward analytic and several-times differentiable functions interpolate them two-dimensional starlike domains parametrized in polar coordinates. radial direction, engage at conformally shift...

A nested sequence of extended Chebyshev spaces possessing Bernstein bases generates an infinite dimension elevation algorithm transforming control polygons of any given level into control polygons of the next level. In this talk, we present our recent results on the convergence of dimension elevation to the underlying Chebyshev-Bézier curve for the case of Müntz spaces [1] and rational function...

In this paper, we introduce the class of $(\beta,\gamma)$-Chebyshev functions and corresponding points, which can be seen as a family {\it generalized} Chebyshev polynomials points. For functions, prove that they are orthogonal in certain subintervals $[-1,1]$ with respect to weighted arc-cosine measure. particular investigate cases where become polynomials, deriving new results concerning clas...

In Euclidean spaces, the geometric notions of nearest-points map, farthestpoints map, Chebyshev set, Klee set, and Chebyshev center are well known and well understood. Since early works going back to the 1930s, tremendous theoretical progress has been made, mostly by extending classical results from Euclidean space to Banach space settings. In all these results, the distance between points is i...