General Composite Implicit Iteration Processes for Common Fixed Points of Asymptotically Nonexpansive Mappings
Yongfu Su, Jia Qing-lan, Hebei Cangzhou, Xiaolong Qin · 2007
Abstract. The purpose of this paper is to introduce the following general composite modified implicit iteration schemes: xn = αnxn−1 + (1 − αn)T nn yn, yn = rnxn−1 + snxn + tnT nn xn−1 + wnT n n xn, rn + sn + tn + wn = 1, {αn}, {rn}, {sn}, {tn}, {wn} ∈ [0, 1], where Tn = TnmodN, for common fixed points of a finite family of asymptot-ically nonexpansive mappings {Ti}Ni=1 in Banach spaces, and to prove weak and strong convergence theorems. The general composite modified implicit iteration scheme presented in this paper included various previous concrete it-eration schemes. Hence, the results presented in this paper extend, generalize and improve the results of Xu and Ori, Oilike, Zhou and Chang, and other authors.