| Shi Yingguang.[J].数学年刊A辑,1980,1(3-4):477~484 |
|
| SIMULTANEOUS BEST RATIONAL AlPPROXIMATION |
| Received:November 07, 1979 |
| DOI： |
| 中文关键词: |
| 英文关键词: |
| 基金项目: |
|
| Hits: 1064 |
| Download times: 0 |
| 中文摘要: |
| |
| 英文摘要: |
| In this paper we discuss the problem of simulta-neons best rational approximation
to a sequence of functions \({f_1},{f_2}, \cdots \in C[a,b]\), i. e. We wish to minimize the expression \({\left\| {{{\left\{ {\sum\limits_{j = 1}^\infty {{\lambda _j}{{\left| {{f_j} - R} \right|}^p}} } \right\}}^{\frac{1}{p}}}} \right\|_\infty }\) ，where \(R \in R_m^n[a,b],1 \le p < \infty ,{\lambda _j} > 0,\sum\limits_{j = 1}^\infty {{\lambda _j}} = 1\). For such a problem we have established the main theorems in the Chebyshey theory, which include the theorems of existence, alternation, de La Vallee Poussin, uniqueness, strong uniqueness as well as that of continuity of the best approximation operator. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
