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Let E be a real Banach space. Let K be a nonempty closed and convex subset of E, T

No abstract

Let E be a real Banach space, K a closed convex nonempty subset of E. Let T 1 , T 2 , . . . , T m : K → K be m total asymptotically nonexpansive mappings. An iterative sequence for approximation of common fixed points (assuming existence) of T 1 , T 2 , . . . , T m is constructed; necessary and sufficient conditions for the convergence of the scheme to a common fixed point of the mappings are given. Furthermore, in the case that E is uniformly convex, a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is established.

Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T 1 , T 2 , . . . , T m : K → K be m total asymptotically nonexpansive mappings. A simple iterative sequence {x n } n≥1 is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti} m i 1 are given. Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence {x n } ∞ n 1 to a common fixed point of the family {Ti} m i 1 is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.