Górnicki, Jarosław A remark on fixed point theorems for Lipschitzian mappings. (English) Zbl 0806.47050 J. Math. Anal. Appl. 183, No. 3, 495-508 (1994). Let \(C\) be a bounded closed convex subset of a \(p\)-uniformly convex Banach space \((p>1)\) and \((a_{n,k})\) be a strongly ergodic matrix. The author proves that every map \(T: C\to C\) satisfying \[ \liminf_{n\to\infty} \inf_ m \sum^ \infty_{k=1} a_{n,k}\| T^{k+m}\|^ p< 1+c \] \((c>0)\) has a fixed point in \(C\). Reviewer: J.Appell (Würzburg) Cited in 3 ReviewsCited in 2 Documents MSC: 47H10 Fixed-point theorems Keywords:strongly ergodic matrix; fixed point PDFBibTeX XMLCite \textit{J. Górnicki}, J. Math. Anal. Appl. 183, No. 3, 495--508 (1994; Zbl 0806.47050) Full Text: DOI