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.

Full text not available from this repository. (Request a copy)

Abstract

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.

[error in script]

IITH Creators: