Relative widths of classes of differentiable functions in theL²metric

Relative average widths of Sobolev spaces in L 2(ℝ d )

“…Recently, Subbotin and Telyakovskii in [13] considered the relative width K 2n (W r C , MW j C , C), where j < r, and the Kolmogorov width d 2n (W r C , C), the minimal multiplier M for which these widths are equal is estimated from above and below. For a positive integer r, MW r C is the class of 2π-periodic functions whose (r − 1)st derivative satisfies the estimate…”

“…In this paper, by combining the ideas of the relative widths and the average widths, we proposed the definition of the relative average width in the sense of Kolmogorov and studied the above-mentioned second problem on the space of Riesz potentials and Bessel potentials in L 2 (R d ) metric as in [12].…”

“…The second problem was studied by Babenko [2] for r = 1, 2 and p = q = 1, by Subbotin and Telyakovskii [11,12] for r ∈ Z + =: {1, 2, . .…”

Relative widths of function classes of L 2(T) defined by a linear differential operator in L q (T)

“…Subbotin and Telyakovskii in [12], [13], [14], Tikhomirov in [18], Babenko in [1], [2], [3], Konovalov in [6], [7], [8], Shevaldin in [17] etc. obtained many results in this field.…”

Linear Relativen-Widths for Linear Operators Preserving an Intersection of Cones

“…Nevertheless, some estimates of relative shapepreserving -widths have been obtained in papers [3][4][5]. Estimates of relative (not necessary shape-preserving) widths have been obtained in works [6][7][8][9][10][11].…”