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.


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)
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