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Convergence and existence results for best proximity points
- Source :
-
Nonlinear Analysis . May2009, Vol. 70 Issue 10, p3665-3671. 7p. - Publication Year :
- 2009
-
Abstract
- Abstract: We provide a positive answer to a question raised by Eldred and Veeramani [A.A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006) 1001–1006] about the existence of a best proximity point for a cyclic contraction map in a reflexive Banach space. Moreover, we introduce a new class of maps, called cyclic -contractions, which contains the cyclic contraction maps as a subclass. Convergence and existence results of best proximity points for cyclic -contraction maps are also obtained. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 70
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 36969993
- Full Text :
- https://doi.org/10.1016/j.na.2008.07.022