Strong convergence theorems for quasi-nonexpansive mappings and maximal monotone operators in Hilbert spaces
Huan-chun Wu, Cao-zong Cheng, De-ning Qu · Journal of Inequalities and Applications · 2014
We present the strong convergence theorem for the iterative scheme for finding a common element of the fixed-point set of a quasi-nonexpansive mapping and the zero set of the sums of maximal monotone operators in Hilbert spaces. Our results extend and improve the recent results of Takahashi et al. (J. Optim. Theory Appl. 147:27-41, 2010) and Takahashi and Takahashi (Nonlinear Anal. 69:1025-1033, 2008). MSC: 47H05, 47H09, 47J25.