Cone-separation and star-shaped separability with applications |
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Authors: | H Mohebi E Naraghirad |
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Institution: | Mahani Mathematical Research Center and Department of Mathematics, University of Kerman, Kerman, Iran |
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Abstract: | Let X be a (real) Banach space, A be a subset of X and x∉A. We present cone-separation in terms of separation by a collection of linear functionals defined on X and obtain necessary and sufficient conditions for cone-separability A and x. Also, we give characterizations for star-shaped separability. Finally, as an application of separability, we characterize best approximation problem by elements of star-shaped sets. |
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Keywords: | 52A30 41A50 46B25 |
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