Sharp inequalities of Jackson type, connected with the best approximation by "angles" of algebraic polynomials have been obtained on the classes of differentiable functions of two variables in the metric of space $L_{2;\rho}({\mathbb{R}}^2)$ of the Chebyshev-Hermite weight.
We obtain certain inequalities of Jackson type, connecting the value of the best approximation of periodic differentiable functions and the generalized modulus of continuity of the highest derivative.
We find the sharp constant in the Jackson-type inequality between the value of the best approximation of functions by trigonometric polynomials and moduli of continuity of m-th order in the spaces Sp, 1 ≤ p < ∞. In the particular case we obtain one result which in a certain sense generalizes the result obtained by L.V. Taykov for m = 1 in the space L2 for the arbitrary moduli of continuity of m-th order (m Є N).
In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of functions in spaces defined on unit sphere.
our central problem is to describe the approximation behavior of functions in spaces for by modulus of smoothness of functions.
In this paper we use the concept of numerical range to characterize best
approximation points in closed convex subsets of B(H): Finally by using this
method we give also a useful characterization of best approximation in
closed convex subsets of a C*-algebra A.
Sharp inequalities of Jackson type in weighted space $L_{2;\rho}({\mathbb{R}}^2)$