Saeidi, Shahram Strong convergence of Browder’s type iterations for left amenable semigroups of Lipschitzian mappings in Banach spaces. (English) Zbl 1222.47086 J. Fixed Point Theory Appl. 5, No. 1, 93-103 (2009). Summary: We study an iterative scheme of Browder’s type for a semigroup of Lipschitzian mappings satisfying some uniform Lipschitzian condition, from a compact convex subset \(C\) of a smooth Banach space into \(C\), with respect to a sequence of strongly asymptotic invariant means defined on an appropriate space of bounded real valued functions of the semigroup. The results presented in this paper generalize the corresponding results of A. T.-M. Lau, H. Miyake and W. Takahashi [Nonlinear Anal., Theory Methods Appl. 67, No. 4, A, 1211–1225 (2007; Zbl 1123.47048)]. Cited in 11 Documents MSC: 47H20 Semigroups of nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H10 Fixed-point theorems 43A07 Means on groups, semigroups, etc.; amenable groups 47A10 Spectrum, resolvent 47J25 Iterative procedures involving nonlinear operators Keywords:amenable semigroup; common fixed point; iteration; left reversible; Lipschitzian mapping; nonexpansive mapping; sunny retraction; strong convergence Citations:Zbl 1123.47048 PDFBibTeX XMLCite \textit{S. Saeidi}, J. Fixed Point Theory Appl. 5, No. 1, 93--103 (2009; Zbl 1222.47086) Full Text: DOI