A Tauberian theorem for the generalized Norlund summability method

ÇANAK İ. , Braha N. L. , Totur U.

GEORGIAN MATHEMATICAL JOURNAL, cilt.27, ss.31-36, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 27 Konu: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1515/gmj-2017-0062
  • Sayfa Sayıları: ss.31-36


Let (p(n)) and (q(n)) be any two non-negative real sequences, with R-n := Sigma(n)(k=0) p(k)q(n-k) not equal 0 (n epsilon N). Let Sigma(infinity)(k=0) ak be a series of real or complex numbers with partial sums (s(n)), and set t(n)(p,q) := 1/R-n Sigma(n)(k=0) p(k)q(n-k)s(k) for n epsilon N. In this paper, we present the necessary and sufficient conditions under which the existence of the limit lim(n ->infinity) s(n) = L follows from that of lim(n ->infinity) t(n)(p, q) = L. These conditions are one-sided or two-sided if (sn) is a sequence of real or complex numbers, respectively.