Convergence theorems for common fixed points of a finite family of total asymptotically nonexpansive nonself mappings in hyperbolic spaces

Abstract

Let C be a nonempty closed convex subset of a complete uniformly convex hyperbolic space X with monotone modulus of uniform convexity h. Let P : X –>C be the nonexpansive retraction. S1,S2, …,Sr :C->X be uniformly L-Lipschitzian and ({vn}, {un}, ξ)-total asymptotically nonexpansive nonself mappings. In this paper, we introduce and study an iterative process for finding common fixed points of the family {Sj}. Assume that F =⌒F(Sj), under certain conditions, strong and 4-convergence of the sequence are proved.