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Strong convergence of Browder’s type iterations for left amenable semigroups of Lipschitzian mappings in Banach spaces. (English) Zbl 1222.47086

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)].

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

Citations:

Zbl 1123.47048
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