Skip Navigation

Journal of the London Mathematical Society 1986 s2-34(1):120-128; doi:10.1112/jlms/s2-34.1.120
© 1986 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Benavides, T. D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© Oxford University Press

Some Properties of the Set and Ball Measures of Non-Compactness and Applications

Tomás Domínguez Benavides

Facultad de Matemáticas, Universidad de Sevilla 41012 Sevilla, Spain

Let X be a metric space. Using the set and ball measures of non-compactness, we define the notions of {alpha}-minimal and ß-minimal sets, and prove that X has an {alpha}-minimal subset. If X is separable, and B is a bounded set of X, we prove that B has a ß-minimal subset A such that ß(A) = ß(B). These results are applied to prove that, if Y is another metric space, T: A -> Y is condensing and {alpha}(A) > 0, then for some k < 1 there exists a non-precompact subset B of A such that T: B -> Y is k-contractive. If X is a separable Hilbert space we prove that, if T:D -> X is set-condensing, then T is ball-condensing, where D is an arbitrary subset of X. Some other relations are proved. We also study the A-properness of several classes of mappings T:D -> X, where D is an arbitrary subset of a Hilbert space, without any surjectivity or boundary restriction on T.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.