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| SIMULTANEOUS BEST RATIONAL AlPPROXIMATION |
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Citation： |
Shi Yingguang.SIMULTANEOUS BEST RATIONAL AlPPROXIMATION[J].Chinese Annals of Mathematics B,1980,1(3-4):477~484 |
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Net amount： 1210 |
Authors： |
Shi Yingguang; |
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| Abstract： |
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. |
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