Jackson-Type Inequalities with Generalized Modulus of Continuity and Exact Values of the n-Widths for the Classes of (ψ, β)-Differentiable Functions in L 2. I

Widths of functional classes defined by majorants of generalized moduli of smoothness in the spaces ${\mathcal S}^p$

“…Later, the problem of finding the exact values of the widths in the spaces L 2 and S p of functional classes of this kind generated by some specific weighting functions µ, was studied in [3], [11,Ch. 4], [30], [31], [14], [8], [13], [25], [27], etc.…”

Direct and inverse approximation theorems in the Besicovitch-Museilak-Orlicz spaces of almost periodic functions

“…In the spaces L 2 of 2π-periodic square-summable functions, for moduli of smoothness ωm (f ; δ), the results of this kind were obtained by Abilov and Abilova [6], and Vakarchuk [32]. Note that in the case f ∈ BS M = L 2 the inequality (3.18) follows from the result of [6] (see Theorem 1).…”

“…In the spaces S p of functions of one and several variables, analogues of Theorem 3.1 and Corollaries 3.1 and 3.3 were proved in [27] and [1], respectively. The inequalities of this type were also investigated in [8,17,27,32,34], etc.…”

Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces

“…In the spaces L 2 , for classical moduli of smoothness inequality (20) was proved by Chernykh [15]. The inequalities of this type were also investigated in [31,32,37,38,25,35,16,6,36,5,3], etc.…”