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- W2341237208 abstract "t_^r, it is required that, for arbitrary e > 0, there exists f£J^ such that sup I F(X) - f(X) |< e for Xe S . In this paper the connection is investigated between existence of such an approximating function and existence of an approximating g e j^~ when for any function e(X) it is required | F(X) — g(X) ^ | e(X) when Xe S. The latter formulation has the advantage of automatically specifying that, at any zero Xo of e(X) on S, g(X0) — F{XQ) and at multiple zeros corresponding derivatives of F and g agree, provided F has derivatives at these points. One interesting application, in case F is continuous and is well-behaved near zeros, is that in which F(X)-f(X)^pF(X) is required, where p denotes a preassigned per cent. Approximation in the real case in which a neighborhood Nξvς2 of F consists of those / such that ξt(x) ^ F(x) — fix) ^ ξ2{x) has been suggested by P.C. Hammer.1 If [|2(B) — !i(&)]/2 is an admissible e(x), the problem reduces to the | e(x) -closeness of approximation" @default.
- W2341237208 created "2016-06-24" @default.
- W2341237208 creator A5006136898 @default.
- W2341237208 date "1965-01-01" @default.
- W2341237208 modified "2023-09-23" @default.
- W2341237208 title "I ε(z) I -CLOSENESS OF APPROXIMATION" @default.
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