Real Analysis Exchange

Some remarks on absolute summability methods

S. M. Mazhar

Abstract

This note deals with certain recent results concerning summability $|\overline{N},p_n|_k$.

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 396-403.

Dates
First available in Project Euclid: 1 June 2012

https://projecteuclid.org/euclid.rae/1338515232

Mathematical Reviews number (MathSciNet)
MR1433625

Zentralblatt MATH identifier
0879.40005

Keywords
Absolute Cesáro summability

Citation

Mazhar, S. M. Some remarks on absolute summability methods. Real Anal. Exchange 22 (1996), no. 1, 396--403. https://projecteuclid.org/euclid.rae/1338515232

References

• H. Bor, On $|\overline{N},p_n|_k$ summability factors of infinite series, Tamkang J. Math. 16 (1985), 13–20.
• H. Bor, On two summability methods, Math. Proc. Cambridge Philos. Soc. 97 (1985), 147–149.
• H. Bor, A note on two summability methods, Proc. Amer. Math. Soc. 98 (1986), 81–84.
• H. Bor, A note on absolute summability methods, Real Anal. Exchange 18 (1992-1993), no. 1, 537–543.
• H. Bor and B. Thorpe, On some absolute summability methods, Analysis 7 (1987), 145–152.
• H. Bor and B. Thorpe, A note on two absolute summability methods, Analysis 12 (1992), 1–3.
• K. Chandrasekharan, The second theorem of consistency for absolutely summable series, Jour. Indian. Math. Soc. 6 (1942), 168–180.
• T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc. 7 (1957), 113–141.
• E. Kogbetliantz, Sur les séries absolument summables par la méthode des moyennes arithmétiques, Bull. Sci. Math. 49 (1925), no. 2, 234–256.
• M. A. Sarigol, 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), 483–489.
• M. A. Sarigol, On the absolute Riesz summability factors of infinite series, Indian J. Pure Appl. Math. 23 (1992), 881–886.
• M. A. Sarigol, Characterization of summability factors for Riesz methods, J. Univ. Kuwait (science) 21 (1994), 1–6.