论文信息 - Fixed point and selection theorems in hyperconvex spaces

Fixed point and selection theorems in hyperconvex spaces

It is shown that a set valued mapping T ∗ of a hyperconvex metric space M which takes values in the space of nonempty externally hyperconvex subsets of M always has a lipschitzian single valued selection T which satisfies d(T (x), T (y)) ≤ dH(T ∗(x), T ∗(y)) for all x, y ∈M . (Here dH denotes the usual Hausdorff distance.) This fact is used to show that the space of all bounded λ-lipschitzian self-mappings of M is itself hyperconvex. Several related results are also obtained.

W. A. Kirk | M. Khamsi | C. M. Yañez

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