New results for best approximation on Banach lattices

Modarres, S. M. S.; Dehghani, M.

doi:10.1016/j.na.2008.05.001

Nonlinear Analysis: Theory, Methods & Applications

2009

DOI: 10.1016/j.na.2008.05.001

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New results for best approximation on Banach lattices

S. M. S. Modarres

M. Dehghani

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2010

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I_m-Quasi Upward Sets, with Their Best Approximations

Iranmanesh

Solimany

2010

Numerical Functional Analysis and Optimization

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The main purpose of this article is to introduce particular subsets of R I , which are not necessarily convex, and we call them I m -quasi upward, or I m -quasi downward. We show that these sets can be translated to downward or upward sets. We introduce the connection of these sets with downward and upward subsets of R I , and discuss the best approximation of these sets. Also we introduce embedded I m -quasi upward and embedded I m -quasi downward subsets of a normed space X .Keywords Banach Lattice Space; Best approximation; Downward set; I m -quasi downward hull; I m -quasi downward set; I m -quasi upward hull; I m -quasi upward set; Proximinal set; Upward set.

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I_m-Quasi Upward Sets, with Their Best Approximations

Iranmanesh

Solimany

2010

Numerical Functional Analysis and Optimization

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show abstract

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New results for best approximation on Banach lattices

Cited by 1 publication

References 7 publications

I_m-Quasi Upward Sets, with Their Best Approximations

I_m-Quasi Upward Sets, with Their Best Approximations

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New results for best approximation on Banach lattices

Cited by 1 publication

References 7 publications

Im-Quasi Upward Sets, with Their Best Approximations

Im-Quasi Upward Sets, with Their Best Approximations

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I_m-Quasi Upward Sets, with Their Best Approximations

I_m-Quasi Upward Sets, with Their Best Approximations