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COMMON FIXED POINTS OF A PAIR OF NON-EXPANSIVE MAPPINGS WITH APPLICATIONS TO CONVEX FEASIBILITY PROBLEMS

  • XIAOLONG QIN (a1), SUN YOUNG CHO (a1) and HAIYUN ZHOU (a2)

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 uC 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: CF is the unique sunny non-expansive retraction from C onto F.

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References

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