Relative Chebyshev point of a system of continuously varying bounded closed sets
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.
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 7, pp 1023-1041.
Citation Example: Hnatyuk Yu. V. Relative Chebyshev point of a system of continuously varying bounded closed sets // Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 889-903.