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Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings

Abstract

Let be a nonempty closed convex subset of a reflexive real Banach space which has a uniformly Gâteaux differentiable norm. Assume that is a sunny nonexpansive retract of with as the sunny nonexpansive retraction. Let , , be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that , , satisfy some mild conditions.

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Correspondence to CE Chidume.

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Chidume, C., Zegeye, H. & Shahzad, N. Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings. Fixed Point Theory Appl 2005, 359216 (2005). https://doi.org/10.1155/FPTA.2005.233

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  • DOI: https://doi.org/10.1155/FPTA.2005.233