A Remark on (C,1) Means of Sequences
نویسندگان
چکیده
tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Let (s n) be a real sequence, let (σ n) denote the sequence of averages of its first n partial sums. Let lim sup n σ n = β and lim inf n σ n = α, where β = α. We prove that lim sup n s n = β and lim inf n s n = α if the following conditions hold: lim λ→∞ lim inf n 1 λ n − n λn k=n+1 (s k − s n) = 0 and lim λ→0 + lim inf n 1 n − λ n n k=λn+1 (s n − s k) = 0, where λ n denotes the integer part of the product λn.
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