Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings.

In this paper, we first introduce a family S = {Sn : C → C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence fxng defined recursively by the algorithm xn+1 = Snxn; n ≥ 1, starting from an initial guess x1 ϵ C, to a common fixed point for such a continuous TAN family S in Banach spaces. Finally, some applications to a finite family of TAN self mappings are also added. [ABSTRACT FROM AUTHOR]