Best approximation by downward sets with applications
- Authors: Rubinov, Alex , Mohebi, Hossein
- Date: 2006
- Type: Text , Journal article
- Relation: Analysis in Theory and Applications Vol. 22, no. 1 (2006), p. 20-40
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- Description: We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x E X and W is a closed downward subset of X.
- Description: C1
- Description: 2003001535
Conical decomposition and vector lattices with respect to several preorders
- Authors: Baratov, Rishat , Rubinov, Alex
- Date: 2006
- Type: Text , Journal article
- Relation: Taiwanese Journal of Mathematics Vol. 10, no. 2 (2006), p. 265-298
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- Description: The decomposition set-valued mapping in a Banach space E with cones K i,i = 1,..., n describes all decompositions of a given element on addends, such that addend i belongs to the i-th cone. We examine the decomposition mapping and its dual. We study conditions that provide the additivity of the decomposition mapping. For this purpose we introduce and study the Riesz interpolation property and lattice properties of spaces with respect to several preorders. The notion of 2-vector lattice is introduced and studied. Theorems that establish the relationship between the Riesz interpolation property and lattice properties of the dual spaces are given.
- Description: C1
- Description: 2003001553
Star-shaped separability with applications
- Authors: Rubinov, Alex , Sharikov, Evgenii
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 13, no. 3-4 (2006), p. 849-860
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- Description: We discuss the notion of a support collection to a star-shaped set at a certain boundary point and a weak separability of two star-shaped sets. Applications to some problems, including the minimization of a star-shaped distance, are given. © Heldermann Verlag.
- Description: C1
- Description: 2003001592