Sentence examples for be a best approximation from inspiring English sources

An element (y_{0} in A) is said to be a best approximation to x if d x,y_{0})=D x,A).

A point (yin M) is said to be a best approximation to (pin X), if (d y,p preceq d z,p)) for all (zin M).

Thus, by Corollary 1 h is a best approximation of f in L 1 ( A, Y ).

Consequently, g ( s ) is a best approximation to f ( s ) in Y for almost every s ∈ A by Corollary 1.

Therefore, there is a best approximation element of x in Y. Thus, Y is proximinal in X. □.

The point x in the theorem above is called a best approximation point of T in A. Note that if (xin A) is a best approximation point, then (|x-Tx|) need not be the optimum.

which is a contradiction so that z = T2z is a best approximation point in A of T A ∪ B → A ∪B.

By the assumption, we know that there is a g in L φ ( A, Y ) which is a best approximation element of f.

Suppose f ∈ L φ ( A, X ) and g is a strongly μ-measurable function such that g ( s ) is a best approximation to f ( s ) from Y for almost everywhere s ∈ A. Then g is a best approximation to f from L φ ( A, Y ).

Since h ( t ) is a best approximation of f ( t ) in Y, and 0 ∈ Y, it follows that ∥ h ( t ) ∥ ≤ 2 ∥ f ( t ) ∥. Therefore, h ∈ L 1 ( A, Y ).

Thus, if (x =eta+xi), (operatorname {dist} x,K) = inf_{eta 'in K} Vert eta+xi-eta'Vert geq Vert xi Vert = Vert x- P x Vert ), showing that (P x)) is a best approximation to x.