Nonlinear ergodic theorems
Nonlinear ergodic theorems
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DOI：
10.1090/s0002-9904-1976-14233-4
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发表时间：
1976-11
影响因子：
1.3
通讯作者：
H. Brezis;F. Browder
中科院分区：
文献类型：
--
作者：
H. Brezis;F. Browder
LEMMA 1.设{xk}和{yk}是H中的两个序列，F是H的非空子集，Cm是{Jj>m {x-}的凸闭包.设（a）对f ∈ F，f ∈ i2 + p（n）0，当k -> °°，对每个m ∈（c）{yk}的无限子列的任何弱极限都在F中.则yk弱收敛到F的一点。引理证明1.因为{yk}是有界的，它足以证明如果F中的f和g是{yk }的无限连续的弱极限，则f = g。对于每一个节点，
LEMMA 1. Let {xk} and {yk} be two sequences in H, F a nonempty subset of H, Cm the convex closure of{Jj>m {x-}. Suppose that (a) ForeachfinF, \xf ƒ i 2 + p ( ƒ) 0 as k —> °° for each m\ (c) Any weak limit of an infinite subsequence of {yk} lies in F. Then yk converges weakly to a point of F. PROOF OF LEMMA 1. Since {yk} is bounded, it suffices to show that if ƒ and g in F are weak limits of infinite subsequences of {yk }, then ƒ = g. For each ƒ,