Proceedings of the American Mathematical Society

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

Author(s): Andrzej Wisnicki; Jacek Wosko
Journal: Proc. Amer. Math. Soc. 124 (1996), 2465-2474.
MSC (1991): Primary 41A65, 46B20, 47H09; Secondary 41A50, 47H10
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 41A65, 46B20, 47H09, 41A50, 47H10

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

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

DOI: 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
Copyright of article: Copyright 1996, American Mathematical Society

Espínola, Rafael; Wi\'snicki, Andrzej; Wo\'sko, Jacek , A geometrical characterization of the $C(K)$ and $C\sb 0(K)$ spaces. , J. Approx. Theory 105 , no. 1 (2000), 87--101. MR 1 768 525

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