Research ArticleOpen AccessGoogle Scholar indexed
Best Simultaneous Approximation of Finite Set in Inner Product Space
Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
- 1 Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
- 2 Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Advances in Pure Mathematics·Volume 03 (2013)·Pages 479–481·Published 23 July 2013·DOI10.4236/apm.2013.35069
Copy link · social · email
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 .
KeywordsBest ApproximationHyperplaneBest Simultaneous Approximation
- F.Deutsch, “Best Approximation in Inner Product Spaces,”Springer, Berlin, 2001.
- D.Fang,X.Luo and Chong Li, “Nonlinear Simultaneous Approximation in Complete Lattice Banach Spaces,”Taiwanese Journal of Mathematics, 2008.
- W. C. Charles, “Linear Algebra,” 1968, p. 62.
- V. Prasolov and V. M. Tikhomirov, “Geometry,” American Mathematical Society, 2001, p. 22.