Semicontractions in locally compact spaces and the case of complex manifolds (Q2452088)

The paper presents several fixed point and periodic point theorems for contraction mappings, local contraction mappings and nonexpansive mappings in metric spaces. The case of a complex Kobayashi hyperbolic manifold is also considered. The approach is based on the so-called \((H_x\)) hypothesis: if \(X\) is a metric space and \(f\) is a self contraction, then \(f\) is said to satisfies the hypothesis \((H_x\)) if, for some \(x\in X\), there exists a convergent sequence \(f^{n_i}(x)\).