Common fixed point theorems for commutings \(k\)-uniformly Lipschitzian mappings in metric spaces (Q2707130)

This article deals with some generalization of Kakutani Ryll Nardzewskii fixed point theorem for a commuting family of weakly continuous and affine mappings. In the article, the authors prove the existence of a common fixed point for mappings from a sequential family of \(k\)-uniformly Lipschitzian mappings defined on bounded metric space \((X,d)\) with a uniform normal convexity structure \({\mathcal F}\) (containing all closed balls of \(X\)) with constant \(\beta\) provided that \(k^2\beta< 1\).