A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings

Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T1, T2, . . . , Tm : K → K bem total asymptotically nonexpansive mappings. A simple iterative sequence {xn}n≥1 is constructed inE and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i 1 are given. Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence {xn}n 1 to a common fixed point of the family {Ti}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.