Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-06T04:24:24.517Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Connectedness of Certain sets in Summability Theory

Published online by Cambridge University Press:  20 November 2018

Mangalam R. Parameswaran
Mangalam R. Parameswaran*
Affiliation:
Dept. of Mathematics and Astronomy the University of Manitoba Winnipeg, R3T 2N2
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note considers the question of the connectedness of the set of limit points of the A-transforms of a sequence, where A is a conservative Hausdorff, quasi-Hausdorff or Meyer-König- Ramanujan type of matrix. New proofs of some known results, as well as some new results are obtained.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 137 - 142
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Barone, H. G.: Limit points of sequences and their transforms by methods of summability, Duke Math. J. 5 (1939), 740-752.Google Scholar
2. Erdös, P. and Piranian, G.: Laconicity and redundancy of Toeplite matrices, Math. Zeit 83 (1964), 381-394.Google Scholar
3. Leviatan, D. and Lorch, L.: On the connectedness of the sets of limit points of certain transforms of bounded sequences. Canad. Math. Bull. 14 (1971), 175-181.Google Scholar
4. Liu, M. and Rhoades, B. E.: Some properties of generalized Hausdorff matrices, Houston J. Math. 2 (1976), 239-250.Google Scholar
5. Parameswaran, M. R.: Some remarks on Borel summability, Quart. J. Math. (Oxford) (2) 10 (1959), 224-229.Google Scholar
6. Parameswaran, M. R.: on the translativity of Hausdorff-and some related methods of summability, J. Indian Math. Soc. 23 (1959), 45-64.Google Scholar
7. Ramanujan, M.. S.: On Hausdorff and quasi-Hausdorff methods of summability, Quart. J. Math. (Oxford) (2) 8 (1957), 197-213.Google Scholar
8. Wells, J. H.: Hausdorft transforms of bounded sequences, Proc. American Math. Soc. 11 (1960), 84-86.Google Scholar