TY - JOUR A2 - Chen, Rudong AU - Su, Juguo AU - Tang, Yuchao AU - Liu, Liwei PY - 2012 DA - 2012/07/05 TI - Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces SP - 170540 VL - 2012 AB - The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes. SN - 1110-757X UR - https://doi.org/10.1155/2012/170540 DO - 10.1155/2012/170540 JF - Journal of Applied Mathematics PB - Hindawi Publishing Corporation KW - ER -