Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths for the classes of $(ψ,β)$-differentiable functions in $L_2$. III

  • B. S. Vakarchuk

Abstract

In the classes $L^{\psi}_{\beta ,2}$ of $2\pi$ -periodic $(\psi , \beta)$-differentiable functions for which $f^{\psi}_{\beta} \in L_2$, we determine the exact constants in Jackson-type inequalities for the characteristic of smoothness $\Lambda_{\gamma} (f, t) = \biggl\{\frac1t \int^t_0 \| \Delta^{\gamma}_ h(f)\|^2dh \biggr\}^{1/2}$, $t > 0$, deternined by averaging the norm of the generalized difference relation $\Delta_{ \gamma}h(f)$. For the classes of $(\psi,\beta)$ -differentiable functions defined by using the characteristic of smoothness $\Lambda_{\gamma}$ and the majorant $\Phi$, satisfying numerous conditions, we find the exact values of some $n$-widths in $L_2$.
Published
25.10.2016
How to Cite
VakarchukB. S. “Jackson-Type Inequalities With Generalized Modulus of Continuity and Exact Values of the $n$-Widths for the Classes of $(ψ,β)$-Differentiable Functions in $L_2$. III”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 10, Oct. 2016, pp. 1299-1, http://umj.imath.kiev.ua/index.php/umj/article/view/1922.
Section
Research articles