doi:10.1155/2007/87414 Research Article Subsequential Convergence Conditions

Let (un) be a sequence of real numbers and let L be any (C,1) regular limitable method. We prove that, under some assumptions, if a sequence (un) or its generator sequence (V (0)n (Δu)) generated regularly by a sequence in a class of sequences is a subsequential convergence condition for L, then for any integer m ≥ 1, the mth repeated arithmetic means of (V (0)n (Δu)), (V (m) n (Δu)), generated regularly by a sequence in the class (m), is also a subsequential convergence condition for L. Copyright © 2007 İbrahim Çanak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1