A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings
C.E. Chidume, Eric U. Ofoedu · International Journal of Mathematics and Mathematical Sciences · 2009
Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T1, T2, …, Tm : K → K be m total asymptotically nonexpansive mappings. A simple iterative sequence is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of are given. Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence to a common fixed point of the family is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.