Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 407651, 26 pages
doi:10.1155/2010/407651
Approximation of common fixed points of a countable family of relatively nonexpansive mappings
Daruni Boonchari1
and Satit Saejung2
1Department of Mathematics, Mahasarakham University, Maha Sarakham 44150, Thailand
2Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
Abstract
We introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting, we not only obtain several convergence theorems announced by many authors but also prove them under weaker assumptions. Applications to the problem of finding a common element of the fixed point set of a relatively nonexpansive mapping and the solution set of an equilibrium problem are also discussed.