Geodesic
On the Chebyshev Center and the Nonemptiness of the Intersection of Nested Sets
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 451-458

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We show that if every bounded set in a Banach space has a Chebyshev center, then the intersection of nested closed bounded sets in this space is nonempty in the case of a critical parameter value. This result generalizes previously obtained sufficient conditions for the nonemptiness of the intersection in the critical case. We also answer a question posed by G. Z. Chelidze and P. L. Papini for Banach spaces satisfying the Opial condition for the weak-$*$ topology.
Keywords: numerical parameter of a set in a normed space, nonemptiness of the intersection of nested sets, Chebyshev center, Opial weak-$*$ property. 
@article{MZM_2022_111_3_a11,
     author = {G. Z. Chelidze and A. N. Danelia and M. Z. Suladze},
     title = {On the {Chebyshev} {Center} and the {Nonemptiness} of the {Intersection} of {Nested} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {451--458},
     publisher = {mathdoc},
     volume = {111},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a11/}
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G. Z. Chelidze; A. N. Danelia; M. Z. Suladze. On the Chebyshev Center and the Nonemptiness of the Intersection of Nested Sets. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 451-458. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a11/