| SHI YINGGUANG.[J].数学年刊A辑,1981,2(2):225~231 |
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| MINIMIZATION AND BEST APPROXIMATION |
| Received:December 10, 1979 |
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| In this paper we discuss the problem of minimization of a nonnegative function F(x, y) of two variables, i.e., we wish to find an element \(P \in M,M \subset C(X)\) being n subspace, to minimize \({\left\| {F(X,P)} \right\|_\infty }\). For such a problem we have established the theorems of existence, alternation and uniqueness. The results obtained here may be effectively applied to the problems of approximation using a generalized weight function, of simultaneous approximation, of approximation with an additive weight, etc. |
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