an:01883741
Zbl 1057.47059
Bugajewski, Dariusz; Esp??nola, Rafael
Measure of nonhyperconvexity and fixed-point theorems
EN
Abstr. Appl. Anal. 2003, No. 2, 111-119 (2003).
00093134
2003
j
47H10 54C20 54E35 54C55
fixed point; hyperconvex; \(\mu\)-measure; \(\mu\)-contractive
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.
Carlos R. Borges (Davis)