Some Properties and Applications of the Hausdorff Distance

A. V. Arutyunov (), S. A. Vartapetov () and S. E. Zhukovskiy ()
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A. V. Arutyunov: Peoples’ Friendship University of Russia
S. A. Vartapetov: Moscow State University
S. E. Zhukovskiy: Peoples’ Friendship University of Russia

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 11, 527-535

Abstract: Abstract Some properties of Hausdorff distance are studied. It is shown that, in every infinite-dimensional normed space, there exists a pair of closed and bounded sets such that the distance between every two points of these sets is greater than the Hausdorff distance between these sets. A relation of the obtained result to set-valued analysis is discussed.

Keywords: Hausdorff metric; Orthogonality in a normed space; Lipschitz continuity; 54C60; 49J52; 54E35 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0732-x

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