Górnicki, Jarosław Fixed points of Lipschitzian semigroups in Banach spaces. (English) Zbl 0894.47044 Stud. Math. 126, No. 2, 101-113 (1997). Let \(E\) be a real \(p\)-uniformly convex Banach space \((p>1)\), \(C\) a bounded closed convex subset of \(E\), and \(T=\{T_s: 0\leq s<\infty\}\) a Lipschitzian semigroup such that \[ \liminf_{\alpha\to\infty} \inf_{\delta\geq 0} {1\over\alpha} \int^\alpha_0\| T_{\beta+\delta}\|^p d\beta< 1+c, \] where \(c\) is some positive constant related to the geometry of \(E\). The author proves then that there is some \(x\in C\) with \(T_sx= x\) for all \(s\geq 0\). Reviewer: J.Appell (Würzburg) MSC: 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H20 Semigroups of nonlinear operators Keywords:Lipschitzian semigroup PDFBibTeX XMLCite \textit{J. Górnicki}, Stud. Math. 126, No. 2, 101--113 (1997; Zbl 0894.47044) Full Text: DOI EuDML