Existence and higher arity iteration for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

摘要

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu (J. Math. Anal. Appl. 333:128-141, 2007) in such a setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and △-convergence results which extend and generalize various corresponding results established in the current literature.