Sezer, Sefa AnilCanak, Ibrahim2020-12-012020-12-0120201012-94052190-76681012-94052190-7668https://doi.org/10.1007/s13370-020-00831-zhttps://hdl.handle.net/11454/61934Let(p(n)) be a sequence of nonnegative numbers such that p(0)>0 and P-n:= Sigma(n)(k=0) pk. the sequence (t(n)) of n-th weighted means of a equence(u(n)) is defined by t(n):=1/P-n (k=0)Sigma(n)p(k)u(k) (n=0,1,2, ...). It is well-known from the Knopp's core theorem that K - core(t) subset of K-core(u) for every real sequence(u(n)). But the converse of this inclusion is not true in general. in this paper, we obtain sufficient conditions under which the converse inclusion holds.en10.1007/s13370-020-00831-zinfo:eu-repo/semantics/closedAccessCore of a sequenceWeighted mean method of summabilityRegularly varying sequence of positive indexArticleWOS:0005663060000012-s2.0-85090236818Q2N/A