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Construction of sunny nonexpansive retractions in Banach spaces

Construction of sunny nonexpansive retractions in Banach spaces

Let  be a commutative family of nonexpansive self-mappings of a closed convex subset C of a uniformly smooth Banach space X such that the set of common fixed points is nonempty. It is shown that if a certain regularity condition is satisfied, then the sunny nonexpansive retraction from C …