数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1531-1540.doi: 10.1016/S0252-9602(16)30088-1

• 论文 • 上一篇    

A SPECIAL MODULUS OF CONTINUITY AND THE K-FUNCTIONAL

Nadezhda DOLMATOVA   

  1. Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
  • 收稿日期:2013-09-30 修回日期:2015-10-22 出版日期:2016-10-25 发布日期:2016-10-25
  • 作者简介:Nadezhda DOLMATOVA,dolmat@math.uni.wroc.pl

A SPECIAL MODULUS OF CONTINUITY AND THE K-FUNCTIONAL

Nadezhda DOLMATOVA   

  1. Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
  • Received:2013-09-30 Revised:2015-10-22 Online:2016-10-25 Published:2016-10-25

摘要:

We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre's K-functional. We also prove Jackson's inequality for the approximation by trigonometric polynomials.

关键词: modulus of continuity, K-functional, Jackson's theorem

Abstract:

We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre's K-functional. We also prove Jackson's inequality for the approximation by trigonometric polynomials.

Key words: modulus of continuity, K-functional, Jackson's theorem

中图分类号: 

  • 42A10