Best proximity pair theorems for relatively nonexpansive mappings

Applied General Topology

Volumn 10, Issue 1, 2009, Pages 21-28

  Raj, V Sankar ^a   Veeramani, P ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Best proximity pair; Cyclic contraction map; Fixed point; Metric projection; Relatively nonexpansive map; Strictly convex space; Uniformly convex banach space

Indexed keywords

EID: 77950794701     PISSN: 15769402     EISSN: 19894147     Source Type: Journal    
DOI: 10.4995/agt.2009.1784     Document Type: Article

References (9)

1. Handbook of metric fixed point theory, Edited by W. A. Kirk and Brailey Sims, Kluwer Acad. Publ., Dordrecht, 2001. MR1904271 (2003b:47002)
2. A. Anthony Eldred, W. A. Kirk and P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171, no. 3 (2005), 283-293. (Pubitemid 43156219)
3. A. Anthony Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006), 1001-1006. (Pubitemid 44688511)
4. M. A. Khamsi and W. A. Kirk, An introduction to metric spaces and fixed point theory, Wiley-Interscience, New York, 2001. MR1818603 (2002b:46002)
5. W. A. Kirk, P. S. Srinivasan and P. Veeramani, Fixed points for mappings satisfying cyclic contractive conditions, Fixed Point Theory 4, no. 1 (2003), 79-89.
6. W. A. Kirk, S. Reich and P. Veeramani, Proximal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim. 24 (2003), 851-862. (Pubitemid 38458024)
7. D. P. Milman and M. S. Brodskii, On the center of a convex set, Dokl. Akad. Nauk. SSSR (N.S) 59 (1948), 837-840.
8. S. Sadiq Basha and P. Veeramani, Best proximity pair theorems for multifunctions with open fiber, J. Approx. Theory. 103 (2000), 119-129. (2000)
9. S. Singh, B. Watson and P. Srivastava, Fixed point theory and best approximation: the KKM-map principle, Kluwer Acad. Publ., Dordrecht, 1997. MR1483076 (99a:47087)