Elamrani, M.; Mbarki, A.; Mehdaoui, B. Common fixed point theorems for commutings \(k\)-uniformly Lipschitzian mappings in metric spaces. (English) Zbl 0978.47039 Southwest J. Pure Appl. Math. 2000, No. 2, 160-171 (2000). 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 \(k^2\beta< 1\). Reviewer: Peter Zabreiko (Minsk) MSC: 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H10 Fixed-point theorems Keywords:Kakutani Ryll Nardzewskii fixed point theorem; commuting family of weakly continuous and affine mappings; common fixed point; \(k\)-uniformly Lipschitzian mappings; normal convexity structure PDFBibTeX XMLCite \textit{M. Elamrani} et al., Southwest J. Pure Appl. Math. 2000, No. 2, 160--171 (2000; Zbl 0978.47039) Full Text: EuDML EMIS