Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2025-01-03T19:16:51.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on a measure of weak noncompactness in the Lebesgue space

Published online by Cambridge University Press:  17 April 2009

Józef Bana´  and
Kishin Sadarangani
Józef Bana´
Affiliation:
Department of Mathematics, Technical University of Rzesz´ow, 35-959 Rzeszów, W. Pola 2, Poland
Kishin Sadarangani
Affiliation:
Department of Mathematical Analysis, University of La Laguna, 38271 La Laguna (Tenerife), Spain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using the concept of equi-integrability we introduce a measure of weak noncompactness in the Lebesgue space L1(0, l). We show that this measure is equal to the classical De Blasi measure of weak noncompactness.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 279 - 286
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Appell, J. and De Pascale, E., ‘Su alcuni parametri connessi con la misura di non compatteza di Hausdorff in spazi di funzioni misurabili’, Boll. Un. Math. Ital. B 6 (1984), 497–515.Google Scholar
[2]Banaś, J., ‘Integrable solutions of Hammerstein and Urysohn integral equations’, J. Austral. Math. Soc. 46 (1989), 61–68.CrossRefGoogle Scholar
[3]Banaś, J. and Rivero, J., ‘On measures of weak noncompactness’, Ann. Mat. Pura Appl. 151 (1988), 213–224.CrossRefGoogle Scholar
[4]De Blasi, F.S., ‘On a property of the unit sphere in Banach spaces’, Bull. Math. Soc. Sci. Math. R. S. Roumaine 21 (1977), 259–262.Google Scholar
[5]Emmanuele, G., ‘Measures of weak noncompactness and fixed point theorems’, Bull. Math. Soc. Sci. Math. R. S. Roumaine 25 (1981), 353–358.Google Scholar
[6]Guerre-Delabriere, S., Classical sequences in Banach spaces, Lecture Notes in Pure and Applied Math. 166 (Marcel Dekker, New York, Basel, Hong Kong, 1992).Google Scholar
[7]Kubiaczyk, I., ‘Kneser type theorems for ordinary differential equations in Banach spaces’, J. Differential Equations 45 (1982), 133–146.CrossRefGoogle Scholar
[8]Lakshmikanthan, V. and Leela, S., Nonlinear differential equations in abstract spaces (Pergamon Press, New York, 1981).Google Scholar