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Best approximation theorems for composites of upper semicontinuous maps

Published online by Cambridge University Press:  17 April 2009

Sehie Park
Sehie Park
Affiliation:
Department of MathematicsSeoul National UniversitySeoul 151–742Korea
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Abstract

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Let (E, τ) be a Hausdorff topological vector space and (X, ω) a weakly compact convex subset of E with the relative weak topology ω. Recently, there have appeared best approximation and fixed point theorems for convex-valued upper semicontinuous maps F: (X, ω) → 2(E, τ) whenever (E, τ) is locally convex. In this paper, these results are extended to a very broad class of multifunctions containing composites of acyclic maps in a topological vector space having sufficiently many linear functionals. Moreover, we also obtain best approximation theorems for classes of multifunctions defined on approximatively compact convex subsets of locally convex Hausdorff topological vector spaces or closed convex subsets of Banach spaces with the Oshman property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 2 , April 1995 , pp. 263 - 272
Copyright
Copyright © Australian Mathematical Society 1995

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