COMMON FIXED POINTS OF A PAIR OF NON-EXPANSIVE MAPPINGS WITH APPLICATIONS TO CONVEX FEASIBILITY PROBLEMS
Xiaolong Qin, Sun Young Cho, Haiyun Zhou · Glasgow Mathematical Journal · 2009
Abstract Let C be a non-empty closed convex subset of a reflexive and strictly convex Banach space E which also has a weakly continuous duality map Jφ(x) with the gauge φ. Let S and T be non-expansive mappings from C into itself such that F = F(S) ∩ F(T) ≠ ∅. Let {αn} and {βn} be sequences in (0, 1). Let {xn} be a sequence defined by where u ∈ C is a given point. Assume that the following restrictions imposed on the control sequences are satisfied: Then the sequence {xn} converges strongly to x* ∈ F, where x* = Q(u) and Q: C → F is the unique sunny non-expansive retraction from C onto F.