An estimate for the least uniform deviation from the class of functions with bounded second derivative

A. V. Mironenko

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An estimate for the least uniform deviation from the class of functions with bounded second derivative

机译：具有有界二阶导数的函数类别的最小均匀偏差的估计

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摘要

We consider the problem of uniform approximation of a continuous function on an interval by means of the class of functions with bounded second derivative. We prove an estimate for the least uniform deviation of a function in terms of its local deviations on uniform and nonuniform three-point grids.

机译：我们通过具有二阶导数的函数类来考虑区间上连续函数的均匀逼近问题。我们证明了函数在均匀和非均匀三点网格上的局部偏差的最小均匀偏差估计。

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来源
《Siberian Mathematical Journal》 |2006年第4期|共14页
作者
A. V. Mironenko;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
uniform approximation; bounded second derivative;

机译：均匀逼近;有界二阶导数;

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1. An estimate for the least uniform deviation from the class of functions with bounded second derivative [J] . A. V. Mironenko Siberian Mathematical Journal . 2006,第4期

机译：具有有界二阶导数的函数类别的最小均匀偏差的估计
2. Asymptotic Expansions of Upper Bounds of Deviations of Functions of Class W~r from Their Generalized Poisson Integrals [J] . Yu.I. Kharkevych Journal of automation and information sciences . 2018,第8期

机译：W〜r类函数的广义泊松积分偏差上界的渐近展开
3. Unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations [J] . Stevi? S. Applied mathematics and computation . 2012,第15期

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4. Coefficient bounds for a new subclass of Bi-univalent functions defined by q-fractional derivative operator [C] . G. Saravanan, K. Muthunagai National Conference on Mathematical Analysis and Computing . 2019

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5. The bounded linear calculus: A characterization of the class of polynomial-time computable functions based on bounded linear logic [D] . Pitt, Francois 1994

机译：有界线性演算：基于有界线性逻辑的多项式时间可计算函数的表征
6. Differences in size structure and function of free and membrane-bound polyribosomes of rat liver. Evidence for a single class of membrane-bound polyribosomes. [O] . J C Ramsey, W J Steele 1977

机译：大鼠肝脏游离和膜结合的多核糖体的大小结构和功能的差异。单类膜结合多核糖体的证据。
7. Estimates of Entropy Numbers and Gaussian Measures for Classes of Functions with Bounded Mixed Derivative [O] . Belinsky E.S. 1998

机译：有界混合微分函数类的熵数估计和高斯测度
8. A Uniform Bound for the Deviation of Empirical Distribution Functions. [R] . Devroye, L. P. 1977

机译：经验分布函数偏差的一致界。

An estimate for the least uniform deviation from the class of functions with bounded second derivative

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