On the Convergence of Composite Implicit Iteration Process with Errors for Symptotically Nonexpansive Mappings in the Intermediate Sense(pp.43-57)

摘要

In this paper we establish a necessary and sufficient condition for the strong convergence of thecomposite iteration process with errors to a common fixed point of the finite family of asymptoticallynonexpansive mappings in the intermediate sense in a arbitrary real Banach space. We also proveseveral strong and weak convergence results of this implicit iterative scheme in a uniformly convexBanach space. Further we also prove that in a uniformly convex Banach space with the dual havingKadec-Klee property, the composite implicit iteration process converges weakly to a common fixedpoint of a finite family of asymptotically nonexpansive mappings in the intermediate sense. Ourresults extend several existing results.