Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings
Tae-Hwa Kim, Yong-Kil Park · Kyungpook mathematical journal · 2009
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 {xn} defined recursively by the algorithm xn+1 = Snxn, n ≥ 1, starting from an initial guess x1 ∈ 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.