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| Paper IPM / M / 436 |
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| Abstract: | |
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By suitable modifying our methods in [10], we prove the following
nonlinear ergodic theorem, extending H. Brezis and F.E. Browder
[4, Theorem 2] and R. Wittmann's mean ergodic theorem [15, Theorem
2.3]. For any sequence (xn)n ≥ 0 in a real Hilbert space H satisfying: (xj|xj+l) ≤ (xk|xk+l)+ϵ(k,l,j−k) for all k,l ≥ 0 and j ≥ k with ϵ bounded and limk,l,m→∞ϵ(k,l,m)=0, and any strongly regular summation mehtod {an,j}, the sequence yn=∑j=0∞an,j xj converges strongly to the same limit. Some identifications of the limit are also given. Download TeX format |
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