Relations on some summability methods

Sulaiman, W. T.

doi:10.1090/S0002-9939-1993-1159178-3

Relations on some summability methods
HTML articles powered by AMS MathViewer

by W. T. Sulaiman PDF

Proc. Amer. Math. Soc. 118 (1993), 1139-1145 Request permission

Abstract:

In this paper we prove a new result connecting the summability methods $|\overline N ,{p_n}{|_k}$ with either $|N,{q_n}{|_k}$ or $|\overline {N,} {w_n}{|_k}$ for given sequences $\{ {p_n}\} , \{ {q_n}\}$, and $\{ {w_n}\}$ of positive real constants. Several results, some of them known, are deduced.

References

Hüseyin Bor, On two summability methods, Math. Proc. Cambridge Philos. Soc. 97 (1985), no. 1, 147–149. MR 764503, DOI 10.1017/S030500410006268X
Hüseyin Bor, A note on two summability methods, Proc. Amer. Math. Soc. 98 (1986), no. 1, 81–84. MR 848880, DOI 10.1090/S0002-9939-1986-0848880-2
H. Bor and B. Thorpe, On some absolute summability methods, Analysis 7 (1987), no. 2, 145–152. MR 885121, DOI 10.1524/anly.1987.7.2.145
G. Das, Tauberian theorems for absolute Nörlund summability, Proc. London Math. Soc. (3) 19 (1969), 357–384. MR 240503, DOI 10.1112/plms/s3-19.2.357
M. A. Sarıgöl, Necessary and sufficient conditions for the equivalence of the summability methods $|\overline N,p_n|_k$ and $|C,1|_k$, Indian J. Pure Appl. Math. 22 (1991), no. 6, 483–489. MR 1117380
W. T. Sulaiman, Notes on two summability methods, Pure Appl. Math. Sci. 31 (1990), no. 1-2, 59–69. MR 1062165