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A note on improved contraction methods for discrete boundary value problems.
- Source :
-
Journal of Difference Equations & Applications . Oct2012, Vol. 18 Issue 10, p1773-1777. 5p. - Publication Year :
- 2012
-
Abstract
- This work investigates a two-point boundary value problem (BVP) involving a first-order difference equation, known as the ‘discrete’ BVP. Some sufficient conditions are formulated under which the discrete BVP will possess a unique solution. The innovation herein involves a strategic choice of metric and utilization of Hölder's inequality. This approach enables the associated mappings to be contractive, which were previously non-contractive in traditional settings. This consequently enables an improved application of the fixed-point theorem of Stefan Banach by addressing a wider range of problems than those covered by the current literature. A YouTube video presentation by the author designed to complement this work is available at http://www.youtube.com/watch?v=luLuQ1KyXy8. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 18
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 80414051
- Full Text :
- https://doi.org/10.1080/10236198.2012.681781