Inequalities between best polynomial approximations and some smoothness characteristics in the space L2 and widths of classes of functions

被引：0
作者：
S. B. Vakarchuk
V. I. Zabutnaya
机构：
[1] Alfred Nobel Dnepropetrovsk University,
[2] Oles Gonchar Dnepropetrovsk National University,undefined
来源：
Mathematical Notes | 2016年 / 99卷
关键词：
best polynomial approximation; smoothness characteristics; Jackson-type inequality; modulus of continuity; Bernstein ; -width of a function class; Rolle’s theorem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We obtain exact constants in Jackson-type inequalities for smoothness characteristics Λk(f), k ∈ N, defined by averaging the kth-order finite differences of functions f ∈ L2. On the basis of this, for differentiable functions in the classes L2r, r ∈ N, we refine the constants in Jackson-type inequalities containing the kth-order modulus of continuity ωk. For classes of functions defined by their smoothness characteristics Λk(f) and majorants Φ satisfying a number of conditions, we calculate the exact values of certain n-widths.
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页码：222 / 242
页数：20
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