Strong convergence theorems for a Mann-type iterative scheme for a family of Lipschitzian mappings

摘要

Let E be a reflexive real Banach space with uniformly Gateaux differentiable norm. Let K be a nonempty closed convex subset of E and T _(nn=1)~∞ be a sequence of L _n -Lipschitzian mappings of K into itself with L _n ≥1, ∑ _(n=1)~∞(L_n-1) < ∞. Let ∩n=1∞F(Tn)≠. Convergence theorems to common fixed points of the family T_(nn=1)~∞ are proved using the Halpern-type iteration process. Corollaries of our theorems present significant improvement of some important recent results (e.g., the results of Aoyama et al. in Nonlinear Anal. 67:2350-2360, 2008).