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Strong convergence to common fixed points of a finite family of asymptotically nonexpansive mappings. (Strong convergence to common fixed points of a finite family of asymptotically nonexpansive map.) (English) Zbl 1219.47135
Summary: Suppose that E is a real Banach space with uniform normal structure and suppose that E has a uniformly Gâteaux differentiable norm. Let C be a nonempty closed convex and bounded subset of E. Let T 1 ,T 2 ,,T r :CC be a finite family of asymptotically nonexpansive mappings. In this paper, we suggest and analyze an iterative algorithm for {T i } i=1 r . We show the convergence of the proposed algorithm to a common fixed point p i=1 r F(T i ) which is the unique solution of some variational inequality. Our results can be considered as an refinement and improvement of many known results.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H05Monotone operators (with respect to duality) and generalizations
47H10Fixed point theorems for nonlinear operators on topological linear spaces