Skip to main content
SpringerLink
Log in

On Mercer's theorem for (C,2)-means

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

A direct proof is given for the following theorem, contained as a special case in a more general result ofPolniakowski:Theorem. Denote σ n the Cesaro-means of order 2 of the sequenceS 1, S2, ... ,α any real number satisfying 0<α<=1. Then\(\mathop { \lim }\limits_{n \to \infty } (\alpha S_n + ((1 - \alpha )\sigma _n ) = S\) implies\(\mathop { \lim }\limits_{n \to \infty } S_n = S\)

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hardy, G. H.: Divergent Series. Oxford: Clarendon Press. 1949.

    Google Scholar 

  2. Klee, K., andP. Szüsz: A Mercerian theorem for Norlund means. Mh. Math.77, 113–119 (1973).

    Google Scholar 

  3. Mercer, F.: On the limits of real variants. Proc. Lond. Math. Soc. (2)5, 206–227 (1907).

    Google Scholar 

  4. Polniakowski, Z.: Polynomial Hausdorff transformations. I. Mercerian theorems. Ann. Math. Polonici5, 1–24 (1958).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State University of New York, 11790, Stony Brook, NY, USA

    P. Szüsz

Authors
  1. P. Szüsz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

To Prof. Th. Schneider on the occasion of his 65th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Szüsz, P. On Mercer's theorem for (C,2)-means. Monatshefte für Mathematik 81, 149–152 (1976). https://doi.org/10.1007/BF01301239

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01301239

Keywords

Search

Navigation