Order summability and almost convergence

Bell, Howard T.

doi:10.1090/S0002-9939-1973-0310489-8

Order summability and almost convergence
HTML articles powered by AMS MathViewer

by Howard T. Bell PDF

Proc. Amer. Math. Soc. 38 (1973), 548-552 Request permission

Abstract:

The object of this paper is to compare the summability methods of almost convergence and order summability. This is done by examining a method of summability which includes both methods. The main result is that every monotone Fourier effective matrix is strongly regular.

References

-summability

W. B. Jurkat and A. Peyerimhoff, Fourier effectiveness and order summability, J. Approximation Theory 4 (1971), 231–244. MR 282142, DOI 10.1016/0021-9045(71)90011-6
W. B. Jurkat and A. Peyerimhoff, Inclusion theorems and order summability, J. Approximation Theory 4 (1971), 245–262. MR 282143, DOI 10.1016/0021-9045(71)90012-8
J. P. King, Almost summable sequences, Proc. Amer. Math. Soc. 17 (1966), 1219–1225. MR 201872, DOI 10.1090/S0002-9939-1966-0201872-6
G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190. MR 27868, DOI 10.1007/BF02393648
S. M. Mazhar and A. H. Siddiqi, On the $F_{A}$ and $A_{B}$ summability of a trigonometric sequence, Indian J. Math. 9 (1967), 461–466 (1968). MR 259482
Paul Schaefer, Matrix transformations of almost convergent sequences, Math. Z. 112 (1969), 321–325. MR 254466, DOI 10.1007/BF01110226

Additional Information

Journal: Proc. Amer. Math. Soc. 38 (1973), 548-552
DOI: https://doi.org/10.1090/S0002-9939-1973-0310489-8
MathSciNet review: 0310489