Vol. 64, No. 2, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Relations between convergence of series and convergence of sequences

Dieter Landers and Lothar Rogge

Vol. 64 (1976), No. 2, 465–469
Abstract

Let A = (an)nN be a sequence of real numbers. For ξ (0,1) define

            ∑n
Sn (ξ,A) :=        ak,  n ∈ N
k=[nξ]+1

where [x] is the greatest integer less than or equal to x. If no ambiguity can arise we write Sn(ξ) instead of Sn(ξ,A). In the theory of regularly varying sequences the problem arose of concluding from the convergence of the sequence Sn(ξ), n N, for all ξ in an appropriate set K (0,1) of real numbers, that the sequence an, n N, converges to zero. In this paper we give some positive results for the case that K consists of two elements.

Mathematical Subject Classification 2000
Primary: 40A05
Milestones
Received: 11 February 1976
Published: 1 June 1976
Authors
Dieter Landers
Lothar Rogge