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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On relative Hausdorff measures
of noncompactness and relative
Chebyshev radii in Banach spaces


Authors: Andrzej Wisnicki and Jacek Wosko
Journal: Proc. Amer. Math. Soc. 124 (1996), 2465-2474
MSC (1991): Primary 41A65, 46B20, 47H09; Secondary 41A50, 47H10
MathSciNet review: 1327052
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Abstract: In this paper we prove some formulae and evaluations on relative Hausdorff measures of noncompactness and relative Chebyshev radii in various Banach spaces. We generalize the Lifschitz constant $\kappa (X)$ and introduce a function $\tilde {\kappa }_X(\cdot )$.


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Additional Information

Andrzej Wisnicki
Affiliation: Department of Mathematics, UMCS, Pl. M. C. Skłodowskiej 1, 20-031 Lublin, Poland
Email: awisnic@golem.umcs.lublin.pl

Jacek Wosko
Affiliation: Department of Mathematics, UMCS, Pl. M. C. Skłodowskiej 1, 20-031 Lublin, Poland
Email: jwosko@golem.umcs.lublin.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03374-6
PII: S 0002-9939(96)03374-6
Keywords: Chebyshev radius, Hausdorff measure of noncompactness, Hausdorff distance, Lifschitz constant, $L^p$ spaces, space of continuous functions.
Received by editor(s): September 19, 1994
Received by editor(s) in revised form: February 24, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society