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| ON THE LEAST DOMINANT CONTINUOUS MODULUS AND ITS APPLICATION |
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Citation： |
Chen Tianpin,Zhu Wenge.ON THE LEAST DOMINANT CONTINUOUS MODULUS AND ITS APPLICATION[J].Chinese Annals of Mathematics B,1996,17(1):73~80 |
| Page view： 997
Net amount： 717 |
Authors： |
Chen Tianpin; Zhu Wenge |
Foundation： |
Project supported by the National Natural Science
Foundation of China and the Doctoral Program of the State
Education Commission of China |
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| Abstract： |
This paper discusses pointwise error estimates for the approximation
by bounded linear operators of continuous functions defined
on compact metric spaces $(X,d)$. The authors introduce a new majorant of the
modulus
of the continuity which is the smallest among those $g(\xi)'$s which have
the following properties
$
\omega(f,\epsilon)\le g(f,\epsilon)\ \text{and}\ g(f,\lambda\epsilon
)\le(1+\lambda)g(f,\epsilon)
$
and by this majorant a new quantitative Korovkin type theorem
on any compact metric space is proved. |
Keywords： |
Quantitative approximation, Modulus of the
continuity,Compact metric space |
Classification： |
41A65 |
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