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Measure of nonhyperconvexity and fixed-point theorems. (English) Zbl 1057.47059
The authors introduce the concept of “measure $$\mu$$ of hyperconvexity of a metric space $$X$$” in order to generalize the Schauder fixed-point theorem in hyperconvex spaces. Of the various interesting results, we quote only Theorem 3.7. Let $$A$$ be a nonempty bounded and complete metric space and let $$f:A\to A$$ be continuous and both $$\alpha$$- and $$\mu$$-contractive. Then $$f$$ has a fixed point. This paper is well-written and contains most of the terminology it uses.

##### MSC:
 47H10 Fixed-point theorems 54C20 Extension of maps 54E35 Metric spaces, metrizability 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
##### Keywords:
fixed point; hyperconvex; $$\mu$$-measure; $$\mu$$-contractive
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