Optimal Recovery and n-Widths for Convex Classes of Functions

Inequalities of Ando's Type for $n$-convex Functions

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

Classes of Convex Functions

We investigate a family that connects various subclasses of functions convex in the unit disk. We also look at generalized sequences for this family.

The Infinite-Dimensional Widths and Optimal Recovery of Generalized Besov Classes

The purpose of the present paper is to consider some weak asymptotic problems concerning the infinite-dimensional Kolmogorov widths, the infinite-dimensional linear widths, the infinite-dimensional Gel’fand widths and optimal recovery in Besov space. It is obvious to be found that the results obtained and methods used in Besov space are easily generalized, and hence in this paper these results ...

Exact Values of Bernstein n-Widths for Some Classes of Convolution Functions

Optimal recovery of isotropic classes of twice-differentiable multivariate functions

Keywords: Optimal recovery of functions Worst-case error Class of twice-differentiable functions Optimal covering a b s t r a c t We consider the class of functions defined on a convex body in R d , d ∈ N, whose second derivatives in any direction are uniformly bounded and the class of d-variate functions periodic with respect to a given full-rank lattice L and having uniformly bounded second d...