Some geometric properties of relative Chebyshev centres in Banach spaces

Daptari, Soumitra and Paul, Tanmoy (2019) Some geometric properties of relative Chebyshev centres in Banach spaces. Contemporary Mathematics, 737. pp. 77-87.

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Abstract. In this paper we characterize Property-(R1), a generalization of 1 1 2 ball property. As a necessary and sufficient condition of a subspace Y with Property-(R1) we derive that r(y,F) = radY (F) + d(y, centY (F)) for any bounded subset F and y ∈ Y . We introduce the notion of modulus of relative chebyshev centre and characterize Property-(R1) in terms of this modulus. It is observed that if Y is a finite co-dimensional subspace of a L1 predual space X and F is a finite subset of X then radY (F) = radX(F)+d(centX(F))+d(F, Y ). We characterize continuity of centV (.) in terms of the modulus of relative chebyshev centre.

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IITH Creators:
IITH CreatorsORCiD
Paul, Tanmoy
Item Type: Article
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 26 Dec 2019 09:08
Last Modified: 26 Dec 2019 09:08
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