Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 471781, 13 pages
doi:10.1155/2010/471781

Halpern's iteration in CAT(0) spaces

Abstract

Motivated by Halpern's result, we prove strong convergence theorem of an iterative sequence in $CAT(0)$ spaces. We apply our result to find a common fixed point of a family of nonexpansive mappings. A convergence theorem for nonself mappings is also discussed.