On (C, 1) means of sequences


Canak I.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.62, no.9, pp.3446-3448, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 9
  • Publication Date: 2011
  • Doi Number: 10.1016/j.camwa.2011.08.060
  • Title of Journal : COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Page Numbers: pp.3446-3448

Abstract

Let (s(n)) be a sequence of real numbers such that lim sup(n) sigma(n) = beta and lim inf(n) sigma(n) = alpha, where sigma(n) = 1/n Sigma(n)(k=1) s(k) and beta not equal alpha. We prove that lim sup(n) s(n) = beta and lim inf(n) s(n) = alpha if the following conditions hold: lim(n) inf 1/[lambda n] - n Sigma([lambda n])(k=n+1) (s(k) - s(n)) >= (beta - alpha) lambda/lambda - 1 for lambda > 1, lim(n) inf 1/n - [lambda n] Sigma(n)(k=[lambda n]+1) (s(k) - s(k)) >= (beta - alpha) lambda/1 -lambda for 0 < lambda < 1, where [lambda n] denotes the integer part of lambda n. (C) 2011 Elsevier Ltd. All right reserved.