For the problem of finding a relative Chebyshev point of a system of continuously varying (in the sense of the Hausdorff metric) bounded closed sets of a normed space linear over the field of complex numbers, we establish some existence and uniqueness theorems, necessary and sufficient conditions, and criteria for a relative Chebyshev point and describe properties of the extremal functional and the extremal operator.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 7, pp. 889–903, July, 2011.
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Hnatyuk, Y.V. Relative Chebyshev point of a system of continuously varying bounded closed sets. Ukr Math J 63, 1023–1041 (2011). https://doi.org/10.1007/s11253-011-0562-4
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DOI: https://doi.org/10.1007/s11253-011-0562-4