Strong convergence theorem for quasi-ϕ-asymptotically nonexpansive mappings in the intermediate sense in Banach spaces
Zhaoli Ma, Lin Wang, Shih-sen Chang · Journal of Inequalities and Applications · 2013
Abstract In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of an infinite family of quasi-ϕ-asymptotically nonexpansive mappings in the intermediate sense in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results. MSC:47H09, 47J25.