in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Discretization of the uniform norm functions from a given finite dimensional subspace continuous is studied. We pay special attention to case trigonometric polynomials with frequencies an arbitrary set fixed cardinality. give two different proofs fact that for any N-dimensional space it sufficient use $$e^{CN}$$ sample points accurate upper bound norm. Previous known results show one cannot imp...

This paper contains some estimates for the integral-uniform norm and the uniform norm of a wide class of random polynomials. The family of integraluniform norms introduced in [6] is a natural generalization of the maximum norm taken over a net. We prove some properties of the integral-uniform norms. The given application of the established estimates demonstrates that the integral-uniform norms ...