Measure of nonhyperconvexity and fixed-point theorems (Q1864361)

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.