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Abstract
In this paper, we find a way to give best simultaneous approximation of n arbitrary points in convex sets. First, we introduce a special hyperplane which is based on those n points. Then by using this hyperplane, we define best approximation of each point and achieve our purpose.
Highlights
As we known, best approximation theory has many applications
We find a way to give best simultaneous approximation of n arbitrary points in convex sets
In [3,4] we can see that a hyperplane of an n-dimensional space is a flat subset with dimension n 1
Summary
One of the best results is best simultaneous approximation of a bounded set but this target cannot be achieved . Frank Deutsch in [1] defined hyperplanes and gave the best approximation of a point in convex sets. In [3,4] we can see that a hyperplane of an n-dimensional space is a flat subset with dimension n 1. In this paper we try to find best simultaneous approximation of n arbitrary points in convex sets. We say theorems of best approximation of a point in convex sets. We give the method of finding best simultaneous approximation of n points in convex set
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