Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 583082, 19 pages
doi:10.1155/2008/583082

Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces

Abstract

The convex feasibility problem (CFP) of finding a point in the nonempty intersection ⋂i=1NCi is considered, where N⩾1 is an integer and the Ci's are assumed to be convex closed subsets of a Banach space E. By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for solving convex feasibility problems in Banach spaces.