Best Approximation by Upward Sets

Volume 14, Issue 4, pp 345-353 http://dx.doi.org/10.22436/jmcs.014.04.08

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2633 Downloads
• 3877 Views

Authors

Zeinab Soltani - Department of Mathematics, Faculty of Scinence, Yasouj University, Yasouj, Iran. Hamid Reza Goudarzi - Department of Mathematics, Faculty of Scinence, Yasouj University, Yasouj, Iran.

Abstract

In this paper we prove some results on upward subsets of a Banach lattice \(X\) with a strong unit. Also we study the best approximation in \(X\) by elements of upward sets, and we give the necessary and sufficient conditions for any element of best approximation, by a closed subset of \(X\).

Share and Cite

Keywords

• Banach lattice
• Best approximation
• Proximinal set
• Upward set.

MSC

•  41A50
•  46B40
•  26B25
•  52A40

References

• [1] H. Alizadeh Nazarkandi, Downward sets and their topological propertices, World Applied Sciences journal , 18(11) (2012), 1630 – 1634.
  • View Article
  • Google Scholar


• [2] H. Asnashari, Two continvity concepts in Approximation Theory, J. Tjmcs, 4 (2012), 32-36.
  • Google Scholar


• [3] C. K. Chui, F. Deutsch, J. D. Ward, Constrained best approximation in Hilbert spaces, Conster. Approx., 6 (1990), 35-64.
  • View Article
  • Google Scholar


• [4] C. K. Chui, F. Deutsch, J. D. Ward, Constrained best approximation in Hilbert spaces II, J. Approx. Theory, 71 (1992), 213-238.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] F. Deutsch, Best approximation in inner product spaces, Springer - Velage, New York (2000)
  • Google Scholar


• [6] F. Deutsch, W. Li, J. D. Ward, A dual approach to constrained in- terpolation from a convex subset of Hilbert spaces, J. Approx. Theory, 90 (1997), 385-414.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] R. A. Halmos, A course on Optimization and Best approximation, CLNM257, Springer (1972)
  • MathSciNet


• [8] V. Jeyakumar, H. Mohebi, Limiting and ε-subgradient characterizations of constrained best approximation, J. Approx. Theory, 135 (2005), 145-159.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] J. E. Martinez - Legaz, A. M. Rubinov, I. Singer, Downward sets and their sepration and approximation properties, J. Global Optimization, 23 (2002), 111-137.
  • View Article
  • MathSciNet
  • Google Scholar


• [10] H. Shojaei, R. Mortezaei, Common Fixed Point for Affine Self Maps Invariant Approximation in P-normed Spaces, J.Tjmcs, 6 (2013), 201-209.


• [11] I. Singer, Abstract convex Analysis, Wiley-Interscience, New York (1987)
  • Google Scholar


• [12] I. Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, New York (1970)
  • MathSciNet
  • Google Scholar


• [13] I. Singer, The theory of best approximation and Functional Analysis, Regional Conference Series in Applied Mathematics, No. 13 (1974)
  • MathSciNet
  • Google Scholar


• [14] B. Z. Vulikh, Introduction to the theory of partially ordered vector spaces, Wolters - Noordhoff, Groningen (1967)
  • View Article
  • Google Scholar