Quasi uniform convexity (QUC) is a geometric property of Banach spaces, introduced in 1973 by J.R. Calder et al., which implies existence of Chebyshev centers for bounded sets. We extend and strengthen some known results about this property. We show that (QUC) is equivalent to existence and continuous dependence (in the Hausdorff metric) of Chebyshev centers of bounded sets. If X is (QUC) then the space C(K;X) of continuous X-valued functions on a compact K is (QUC) as well. We also show that a sufficient condition introduced by L. Pevac already implies (QUC), and we provide a couple of new sufficient conditions for (QUC). Together with Chebyshev centers, we consider also asymptotic centers for bounded sequences or nets (of points or sets).
Quasi uniform convexity : Revisited / L. Vesely. - In: JOURNAL OF APPROXIMATION THEORY. - ISSN 0021-9045. - 223(2017 Nov), pp. 64-76.
|Titolo:||Quasi uniform convexity : Revisited|
|Parole Chiave:||approximate center; Chebyshev center; Quasi uniformly convex Banach space; analysis; numerical analysis; mathematics (all); applied mathematics|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||nov-2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.jat.2017.08.002|
|Appare nelle tipologie:||01 - Articolo su periodico|