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Fixed point properties for semigroups of nonlinear mappings on unbounded sets
- Source :
- Journal of Mathematical Analysis and Applications 433 (2016), 1204-1219
- Publication Year :
- 2020
-
Abstract
- A well-known result of W. Ray asserts that if $C$ is an unbounded convex subset of a Hilbert space, then there is a nonexpansive mapping $T$: $C\to C$ that has no fixed point. In this paper we establish some common fixed point properties for a semitopological semigroup $S$ of nonexpansive mappings acting on a closed convex subset $C$ of a Hilbert space, assuming that there is a point $c\in C$ with a bounded orbit and assuming that certain subspace of $C_b(S)$ has a left invariant mean. Left invariant mean (or amenability) is an important notion in harmonic analysis of semigroups and groups introduced by von Neumann in 1929 \cite{Neu} and formalized by Day in 1957 \cite{Day}. In our investigation we use the notion of common attractive points introduced recently by S. Atsushiba and W. Takahashi.<br />Comment: 22 pages. arXiv admin note: text overlap with arXiv:2001.08149
Details
- Database :
- arXiv
- Journal :
- Journal of Mathematical Analysis and Applications 433 (2016), 1204-1219
- Publication Type :
- Report
- Accession number :
- edsarx.2001.08158
- Document Type :
- Working Paper