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Takahashi [10] introduced a notion of convexity in metric spaces and studied some fixed point theorems for nonexpansive mappings in such spaces. Let X be a metric space and I = [0, 1]. A mapping W: X ×X × I → X is said to be a convex structure on X if for each (x, y, λ) ∈ X ×X × I and u ∈ X,
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Shimizu et al. (1996) studied this question.
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