Abstract
In view of Kogbetliantz's identity [7] the absolute Cesáro summability of orderk (k)>−1) of an infinite seriesΣ a n is the same as the absolute convergence ofΣ(τ k n )n −1 whereτ k n is then-th Cesáro mean of orderk of sequence {na n }.Das [5] has shown that similar dependence is true for certain classes of Nörlund means. The object of this paper is to establish two theorems on absolute summability factors involving two lower-semimatrix transformations and thereby to generalise a result ofChow [3] on absolute Cesáro summability factors and a result ofBosanquet andDas [1] on absolute Harmonic summability factors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bosanquet, L. S., andG. Das.: Absolute summability factors for Nörlund means. J. London Math. Soc. (to appear).
Cooke, R. C.: Infinite matrices and sequence spaces. Macmillan, 1950.
Chow, H. C.: Note on convergence and summability factors. J. London Math. Soc.29, 459–476 (1954).
Das, G.: Absolute summability factors and inverse of certain matrices, to appear.
Das, G.: Tauberian theorem for absolute Nörlund summability. Proc. London Math. Soc.19, 357–384 (1969).
Das, G., V. P. Srivastava, andR. N. Mohapatra: On absolute summability factors of infinite series. J. Indian Math. Soc.29, 189–200 (1967).
Kogbetliantz, E.: Sur les series absolument sommables par la méthode des moyennes arithmetiques. Bull. Sci. Math. (2),49, 234–256 (1925).
Knopp, K., undG. G. Lorentz: Beiträge zur absoluten Limitierung. Arch. Math.2, 234–256 (1925).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mohapatra, R.N., Das, G. Summability factors for lower-semi-matrix transformations. Monatshefte für Mathematik 79, 307–315 (1975). https://doi.org/10.1007/BF01647332
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01647332