کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4614922 | 1339303 | 2016 | 16 صفحه PDF | دانلود رایگان |
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→CC→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∈Cc∈C with a bounded orbit and assuming that certain subspace of Cb(S)Cb(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 [28] and formalized by Day in 1957 [5]. In our investigation we use the notion of common attractive points introduced recently by S. Atsushiba and W. Takahashi.
Journal: Journal of Mathematical Analysis and Applications - Volume 433, Issue 2, 15 January 2016, Pages 1204–1219