The Near-Ring of Lipschitz Functions on a Metric Space
Joint Authors
Farag, Mark
van der Merwe, Brink
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-07-13
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
This paper treats near-rings of zero-preserving Lipschitz functions on metric spaces that are also abelian groups, using pointwise addition of functions as addition and composition of functions as multiplication.
We identify a condition on the metric ensuring that the set of all such Lipschitz functions is a near-ring, and we investigate the complications that arise from the lack of left distributivity in the resulting right near-ring.
We study the behavior of the set of invertible Lipschitz functions, and we initiate an investigation into the ideal structure of normed near-rings of Lipschitz functions.
Examples are given to illustrate the results and to demonstrate the limits of the theory.
American Psychological Association (APA)
Farag, Mark& van der Merwe, Brink. 2010. The Near-Ring of Lipschitz Functions on a Metric Space. International Journal of Mathematics and Mathematical Sciences،Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-460324
Modern Language Association (MLA)
Farag, Mark& van der Merwe, Brink. The Near-Ring of Lipschitz Functions on a Metric Space. International Journal of Mathematics and Mathematical Sciences No. 2010 (2010), pp.1-14.
https://search.emarefa.net/detail/BIM-460324
American Medical Association (AMA)
Farag, Mark& van der Merwe, Brink. The Near-Ring of Lipschitz Functions on a Metric Space. International Journal of Mathematics and Mathematical Sciences. 2010. Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-460324
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460324