Strong convergence theorems for modifying Halpern iterations for a totally quasi-ϕ-asymptotically nonexpansive multi-valued mapping in reflexive Banach spaces
Hong Bo Liu, Yi Li · Journal of Inequalities and Applications · 2013
In this paper, we discuss an iterative sequence for a totally quasi- ϕ -asymptotically nonexpansive multi-valued mapping for modifying Halpern’s iterations and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Appl. Math. Comput. 218:6489-6497, 2012). MSC: 47J05, 47H09, 49J25.