The phrase "a best approximation" is correct and usable in written English.
It can be used when discussing a value or estimate that is considered the closest or most accurate representation of something, often in mathematical or scientific contexts.
Example: "The model provides a best approximation of the data trends observed over the last decade."
Alternatives: "the closest estimate" or "the most accurate representation".
A best approximation theorem provides us with best approximate solutions which is not necessarily optimal.
A best approximation theorem guarantees the existence of an approximate solution, a best proximity point theorem is contemplated for solving the problem to find an approximate solution which is optimal.
In fact, in the setting of a metric space ((X,d)), if (T A to X), then a best approximation theorem provides sufficient conditions that confirm the existence of an element (x_{0}), known as the best approximant, such that (d(x_{0},Tx_{0}) = d(Tx_{0},A)), where (d(A,B):=inf{d x,y) : x in A text{ and } y in B}) for any nonempty subsets A and B of X.
A best approximation is given by (1.1).
In this case y is called a best approximation of x in Y.
Thus, by Corollary 1 h is a best approximation of f in L 1 ( A, Y ).
Given the limitations imposed by the lack of a ground truth for real-world networks for which the community structure is unknown, the approaches we adopted to assess the results are only a best-approximation of any robust evaluation method.
Despite these limitations, however, for each drug we established a best-approximation average dose on the basis of the literature and official statistics.
Then, by Theorem 3.2, every increasing f : [ u 0, v 0 ] → ℓ 2 has a minimum best approximation point and a maximum best approximation point with respect to W ( x, y ) in [ u 0, v 0 ].
Given u 0, v 0 ∈ L 2 such that u 0 ≺ v 0 ; then, by Theorem 3.2, every increasing f : [ u 0, v 0 ] → L 2 has a minimum best approximation point and a maximum best approximation point with respect to W ( x, y ) in [ u 0, v 0 ].
In 1969, Fan [6] introduced the notion of a best proximity and established a classical best approximation theorem.
